doc. RNDr. Oldřich Semerák, Ph.D., DSc.


adresa:
Ústav teoretické fyziky
Matematicko-fyzikální fakulta Univerzity Karlovy
V Holešovičkách 2
180 00 Praha 8
kancelář:
A1043
telefon:
+420 95155 2506
e-mail:
oldrich.semerak@matfyz.cuni.cz
www:
MFF UK

Odborné zájmy

general relativity
relativistic astrophysics
black-hole space-times

Vyučované předměty

Nabídka závěrečných prací

Vypsané a  vedené práce v SISu

Studenti

Bakalářští studenti

Magisterští studenti

Doktorští studenti

Text k předmětu Specialni TEORIE RELATIVITY:

STR.pdf

POZNÁMKY:

  • Text pokrývá víceméně přesně látku vyučovanou v kursu Speciální teorie relativity (NOFY023).
  • Omlouvám se, že stále chybějí obrázky, snad brzy doplním...

 

Lecture notes to GENERAL THEORY OF RELATIVITY, RELATIVISTIC PHYSICS I and RELATIVISTIC PHYSICS II:

GTR.pdf

REMARX:

  • Notes cover the first two semesters of GR (Obecná teorie relativity, NTMF111; and Relativistická fyzika I, NTMF037) and some topics of the third semester (Relativistická fyzika II, NTMF038). They do not (yet) include most of the topics usually covered by student talks. Will try to also add these gradually.
    Text has not "suffered" any serious check, so will be grateful for corrections, suggestions...
    Some references to other sections are not working (?? being displayed) -- it is typically because the respective sections do not yet exist.
    Bibliography is by far not complete, it has been included in an opportune way.
    Figures 2.1 and 6.2 are slightly misplaced; have been fighting with that without success. Apparently bounding box (they are eps) is not recognized correctly (though it IS there and correct).
  • 5th November 2020: Section 13.7.1 and Reissner-Nordström added.
  • 16th November: Kerr and "More on motion in black-hole fields" chapters added, together with Appendix B.
    • 18th November: Section 17.2.7 added, plus a few corrections.
  • 4th January 2021: Chapter on Black holes & gravitational collapse added (see Fig. 18.2 on energy extraction employing a perfect Bosch dynamo!), plus part of the chapter on Relativistic stellar models (as far as the TOV equation). Beware, I changed notation for the Killing vector fields in stationary and axisymmetric space-times: instead of "eta" and "xi", am now denoting them "t" and "phi" (with respective index) -- hope it is suggestive.
  • 11th January: Chapter on Relativistic stellar models written as far as Equation for energy transfer (still missing is the section on Radial oscillations).
    I have changed notation for cyclic permutation of indices from the cumbersome [...]cycl to {...}. It is described in Preface / notation part.
  • 1st February: Chapter on Relativistic stellar models finished, and chapters on Final stages of stellar evolution and on Lagrangian formulation added. Therefore, all lectures of the first two GR semesters have been covered.
    Besides that, short (but important) section 7.6 has been added, also something at the end of A.1.1. And hope you will like new figures (e.g. in Preface).
    Thanks go to Matěj Mezera for several corrections.
  • 23rd February: Chapter on Fermi-Walker transport added (applications are not compulsory; may use them next semester for seminar), plus several minor corrections.
    Thanks to Jan Střeleček and Richard Ivánek for corrections.
  • 15th March: Chapters 23 (Vector fields and their integral congruences) and 24 (3+1 splitting of space-time) added. Plus minor corrections throughout.
    Thanks to Valerie Tynianski for noticing a mistake.
  • 18th March: correcting misprints in the chapter on geodesics (thanks to Jonáš Dujava).
  • 25th March: Chapter 25 (Hamiltonian formalism in GR) included, and section on surface term in Chapter 22 (Lagrangian formalism) added. New figure 24.1 in the (3+1)-splitting Chapter.
  • 6th April: Chapter on Linearised theory and gravitational waves added (now it is Chapter 22), with its last (-but-one possibly) section yet to be done. Plus occassional editing at various places.
  • 12th April: Chapter on Linearised theory and gravitational waves continued, just would like to finish its "Gravitoelectromagnetism" section. Thanking again Matěj Mezera for several corrections.
  • 19th April: Chapter on Linearised theory and gravitational waves finished.
  • 23rd April: Section 23.1 (Action and the functional derivative) added and, at the beginning of Chapter 26 (Hamiltonian formulation), the generic name for configuration variables (fields) changed from "q" to "psi", in order to be consistent with Section 23.1.
  • 7th May: Many minor modifications, plus Kandinsky ("Weighing down", featuring the "=" sign) added after the Einstein equations. Thanks to Jonáš Dujava for comments.
  • 11th May: Section on Shapiro time delay added after apsidal advance and light bending. And paragraph on principal null directions (17.3.7) modified in normalization of the principal fields. (Thanks to Valerie Tynianski for discussion and checking.)
  • 25th May: Have simplified derivation in the Frobenius-theorem section, and also (thanks to Jonáš Dujava) "proof" of the planarity of geodesic motion in Schwarzschild.
  • 2nd June: Algebraic classification of tensor fields started. Plus minor corrections elsewhere (mainly in the Frobenius-theorem section).
  • 11th October: Several corrections at various places, mainly due to Jonáš Dujava.
  • 7th January 2022: Algebraic classification continued (Goldberg-Sachs theorem still remains to be proven), "Palatini's" variational method (hopefully) treated in a simpler way, certain extension in the null-congruence section. Plus various minor corrections -- thanks go mainly to Róbert Jurčík. "Bez názvu" by Václav Boštík added at the end by obvious reason.
  • 14th February 2022: Edit in "Effect of gravitational waves on test particles" section, thanks to Michael Vávra.
  • 31st March 2022: Minor error corrected in "d'Alembert gamma_{0j}" equation above eq. (22.37) (and, consequently, in 22.37 itself) in the Gravitoelectromagnetism section, thanks to Šimon Pajger. Plus minor edit in the Newtonian limit of Einstein equations. Plus still fighting with (simple proof of) the Goldberg-Sachs theorem... (standardly it is being proved in Newman-Penrose formalism, which I however do not want to employ).
  • 8th May 2022: Several corrections of minor mistakes, otherwise nothing new.
  • 31st October 2022: Several corrections of minor mistakes, nothing really new.
  • 23rd December 2022: Minor corrections, somewhat more concise "Palatini's variational method".
  • 20th January 2023: "Palatini's variational method" improved even more thanks to Jonáš Dujava.
  • 4th April 2023: There are always mistakes to correct...
  • 12th October 2023: Several improvements thanks to Marek Milička.
  • 21st November 2023: Few corrections thanks to Karel Balej. A short paragraph on acceleration of circular motion (specifically on the "repulsive" effect at the very centre) in Kerr added. The (summer) long list of comments from Jonáš Dujava still to be tackled...
  • 18th March 2024: Quite some changes: new chapter on Conservation laws added. (Note: still certain details on Lie derivative should be fixed, also in the Lie-derivative chapter. -Thanks to Pavel Krtouš for discussions.) Part of a new chapter on Initial (Cauchy) problem added (GR case still to be covered). And, few corrections thanks to Viktor Vařeka (mainly on Carter observers, in the Kerr section).
  • 25th March 2024: Cauchy problem for GR finished, just a "summarizing theorem" yet to be added.
  • 15th April 2024: Various improvements in the Conservation-laws chapter (also adjusting signs in definitions to match the rest of the notes), the "Pseudotensor" section yet to be done. Cauchy problem for GR finished completely.
  • 30th April 2024: Various improvements in the Conservation-laws chapter (the section on Landau-Lifshitz pseudotensor rewritten), several changes in the Hamiltonian-formalism chapter. Some additions to the chapter on Lie derivative (Lie derivative of the affine connection etc.) A short section on Geometrical objects added to the chapter on fundamental principles.
  • 14th May 2024: Slight improvements mainly in chapters on Hamiltonian formalism and Algebraic classification. Heroic section 28.2.5. corrected and completed!
  • 21st May 2024: Slight additions in the Algebraic classification chapter.
  • 29th November 2024: VERY helpful remarks by Jonáš Dujava "implemented", at last! Plus a few minor improvements.
  • 9th December 2024: Another incredible progress: hyperreferences. Have had to delete all the maths in section titles, now it should work. Enjoy :-)
  • 3rd February 2025: Again incredible: the Goldberg-Sachs theorem proved at last! Who invents shorter way will be punished somehow. (Just being obstinate, the whole chapter on algebraic classification is not in fact covered within the course.) And thanks to Karel Kraus, David Podrápský and mainly Marek Milička for comments.
  • 25rd February 2025: Many minor changes, I think useful at times.
  • 16th April 2025: Have quite rewritten (and still rewriting) the chapter on Conservation laws. (Also minor changes in the 3+1 splitting and in Hamiltonian formalism.) Am grateful to the current course audience for comments, especially Marek, Josef and Vendelín.
  • 22nd April 2025: First, Section 28.10 rewritten without using the Lie derivative of affine connection (have shifted all this stuff to 11.3.3, together with some new efforts). Second, in Chapter 23 (on Lagrangian formulation of Einstein equations), I have re-denoted all the variations as the ``barred'' ones (\bar\delta), taken ``at the same x'', consistently with the notation used in Chapter 28 on conservation laws. Third, Section 28.10.1 has been somewhat rewritten.
  • 14th May 2025: Chapter 29 on relativistic strings added, not yet complete.
  • 2nd July 2025: Chapter 29 on relativistic strings kind of completed. Lead by Brandon Carter's arXiv notes, I added the ``geometrical'' part where the main result is that the equations of motion can be written elegantly as the vanishing of the mean-curvature vector of the world-sheet.
  • 7th July 2025: Encouraged by Josef Trojan, I have supplemented the chapter on Hamiltonian formalism by sections 27.2.5 and 27.2.6 on boundary part of the Hamiltonian and ADM integral quantities.
  • 4th August 2025: Chapter 29 on strings improved, mainly in the 2+2 view of the world-sheet. Grateful to Jan Hrubeš for comments.
  • 20th August 2025: Section on Israel's junction conditions added to the chapter on 3+1 decomposition. The light-like version may also be provided in future, and some examples.
  • 26th August 2025: Junction conditions on null hypersurfaces added (Section 25.7.3).
  • 28th August 2025: In junction conditions, example of the Oppenheimer-Snyder collapse added. Looking forward to 666 pages of the file.

 

Notes on black-hole Killing horizons (part of BLACK-HOLE THERMODYNAMICS course in 2025):

Literatura

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Seznam publikací s afiliací ÚTF

  1. Kotlařík, P.; Kofroň, D.; Semerák, O.: Static Thin Disks with Power-law Density Profiles ApJ 931 (2022) DOI
  2. Bičák, J.; Kofroň, D.; Semerák, O.: Trojí vzpomínání na Jiřího Langera Czech. J. Phys. 70 (2020)
  3. Semerák, O.; Čížek, P.: Rotating Disc around a Schwarzschild Black Hole Universe 6 (2020) DOI
  4. Huré, J.-M.; Basillais, B.; Karas, V.; Trova, A.; Semerák, O.: The exterior gravitational potential of toroids Mon. Not. R. Astron. Soc. 494 (2020) DOI
  5. Polcar, L.; Suková, P.; Semerák, O.: Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V ApJ 877 (2019) DOI
  6. Semerák, O.; Basovník, M.; Kotlařík, P.: Schwarzschild binary supported by an Appell ring Phys. Rev. D  99 (2019) DOI
  7. Polcar, L.; Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method Phys. Rev. D  100 (2019) DOI
  8. Kotlařík, P.; Semerák, O.; Čížek, P.: Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution Phys. Rev. D  97 (2018) DOI
  9. Costa, L. F. O.; Lukes-Gerakopoulos, G.; Semerák, O.: Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition Phys. Rev. D  97 (2018) DOI
  10. Čížek, P.; Semerák, O.: Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk ApJS 232 (2017) DOI
  11. Semerák, O.; Basovník, M.: Geometry of deformed black holes. I. Majumdar-Papapetrou binary Phys. Rev. D  94 (2016) DOI
  12. Basovník, M.; Semerák, O.: Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring Phys. Rev. D  94 (2016) DOI
  13. Semerák, O.: Static axisymmetric rings in general relativity: How diverse they are Phys. Rev. D  94 (2016) DOI
  14. Semerák, O.: Approximating Light Rays in the Schwarzschild Field ApJ 800 (2015) DOI
  15. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Particles under radiation thrust in Schwarzschild space–time from a flux perpendicular to the equatorial plane Mon. Not. R. Astron. Soc. 446 (2015) DOI
  16. Witzany, V.; Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – IV Mon. Not. R. Astron. Soc. 451 (2015) DOI
  17. Semerák, O.: Albert Einstein a století obecné relativity Pokroky Mat. Fyz. Astron. 60 (2015)
  18. Semerák, O.; Šrámek, M.: Spinning particles in vacuum spacetimes of different curvature types Phys. Rev. D  92 (2015) DOI
  19. Semerák, O.: Spinning particles in vacuum spacetimes of different curvature types: Natural reference tetrads and massless particles Phys. Rev. D  92 (2015) DOI
  20. Suková, P.; Semerák, O.: Free motion around black holes with discs or rings: between integrability and chaos – III Mon. Not. R. Astron. Soc. 436 (2013) DOI
  21. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – II Mon. Not. R. Astron. Soc. 425 (2012) DOI
  22. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.; Stella, L.: The general relativistic Poynting–Robertson effect: II. A photon flux with nonzero angular momentum Class. Quantum Grav. 28 (2011) DOI
  23. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Effect of radiation flux on test-particle motion in the Vaidya spacetime Class. Quantum Grav. 28 (2011) DOI
  24. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability Mon. Not. R. Astron. Soc. 404 (2010) DOI
  25. Kyrian, K.; Semerák, O.: Spinning test particles in a Kerr field - II Mon. Not. R. Astron. Soc. 382 (2007) DOI
  26. Šácha, J.; Semerák, O.: Toroidal source around a static black hole Czech. J. Phys. 55 (2005) DOI
  27. Semerák, O.: Albert Einstein a století moderní fyziky Pokroky Mat. Fyz. Astron. 50 (2005)
  28. Semerák, O.: Exact power-law discs around static black holes Class. Quantum Grav. 21 (2004) DOI
  29. Karas, V.; Huré, J.-M.; Semerák, O.: TOPICAL REVIEW: Gravitating discs around black holes Class. Quantum Grav. 21 (2004) DOI
  30. Semerák, O.: Gravitating discs around a Schwarzschild black hole: III Class. Quantum Grav. 20 (2003) DOI
  31. Semerák, O.: Expulsion of external fields from extreme horizons: Example of an external gravitational field Czech. J. Phys. 52 (2002) DOI
  32. Žáček, M.; Semerák, O.: Gravitating discs around a Schwarzschild black hole II Czech. J. Phys. 52 (2002) DOI
  33. Semerák, O.: Thin disc around a rotating black hole, but with support in-between Class. Quantum Grav. 19 (2002) DOI
  34. Semerák, O.; Zellerin, T.; Žáček, M.: Erratum: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 322 (2001) DOI
  35. Semerák, O.: Curvature singularity around first Morgan-Morgan disc Class. Quantum Grav. 18 (2001) DOI
  36. Semerák, O.; Žáček, M.: Gravitating discs around a Schwarzschild black hole: I Class. Quantum Grav. 17 (2000) DOI
  37. Zellerin, T.; Semerák, O.: Two-soliton stationary axisymmetric sprouts from Weyl seeds Class. Quantum Grav. 17 (2000) DOI
  38. Semerák, O.; Žáček, M.: Oscillations of Static Discs around Schwarzschild Black Holes: Effect of Self-Gravitation Publ. Astron. Soc. Jpn. 52 (2000) DOI
  39. Semerák, O.; Karas, V.: Pseudo-Newtonian models of a rotating black hole field A&A 343 (1999)
  40. Semerák, O.; Zellerin, T.; Žáček, M.: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  41. Semerák, O.; Žáček, M.; Zellerin, T.: Test-particle motion in superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  42. Semerák, O.: Spinning test particles in a Kerr field - I Mon. Not. R. Astron. Soc. 308 (1999) DOI
  43. Semerák, O.; Karas, V.; de Felice, F.: Parameters of Black Holes in Sources with Periodic Variability Publ. Astron. Soc. Jpn. 51 (1999) DOI
  44. Semerák, O.: COMMENT: Gravitomagnetic clock effect and extremely accelerated observers Class. Quantum Grav. 16 (1999) DOI
  45. Semerák, O.: Rotospheres in Stationary Axisymmetric Spacetimes Ann. Phys. 263 (1998) DOI
  46. Semerák, O.: Circular Orbits in Stationary Axisymmetric Spacetimes Gen. Relativ. Gravit. 30 (1998) DOI
  47. Semerák, O.; Bičák, J.: The interplay between forces in the Kerr-Newman field. Class. Quantum Grav. 14 (1997)
  48. Semerák, O.: Forces at the Kerr singularity Ap&SS 250 (1997) DOI
  49. Semerák, O.: Gyroscope on Polar Orbit in the Kerr Field Gen. Relativ. Gravit. 29 (1997) DOI
  50. Semerák, O.; de Felice, F.: Quasi-local measurements and orientation in black-hole fields Class. Quantum Grav. 14 (1997) DOI
  51. Semerák, O.: Collimation (and Other) Effects of the Kerr Field: an Interpretation Astrophys. Lett. Commun. 33 (1996)
  52. Semerák, O.: Photon escape cones in the Kerr field Helv. Phys. Acta 69 (1996)
  53. Semerák, O.: Extremally Accelerated Observers in Stationary Axisymmetric Spacetimes Gen. Relativ. Gravit. 28 (1996) DOI
  54. Semerák, O.: What forces act in relativistic gyroscope precession? Class. Quantum Grav. 13 (1996) DOI
  55. Semerák, O.: Some aspects of motion in the Kerr field Czech. J. Phys. 45 (1995) DOI
  56. Semerák, O.: What forces drive the relativistic motion? Nuovo Cim. B  110 (1995) DOI
  57. Semerák, O.: On the occurrence of rotospheres in the Kerr field Phys. Scr. 52 (1995) DOI
  58. Semerák, O.: On the competition of forces in the Kerr field A&A 291 (1994)
  59. Bičák, J.; Semerák, O.; Hadrava, P.: Collimation Effects of the Kerr Field Mon. Not. R. Astron. Soc. 263 (1993) DOI
  60. Semerák, O.: Stationary frames in the Kerr field Gen. Relativ. Gravit. 25 (1993) DOI
doc. RNDr. Oldřich Semerák, Ph.D., DSc.
adresa:
Ústav teoretické fyziky
Matematicko-fyzikální fakulta Univerzity Karlovy
V Holešovičkách 2
180 00 Praha 8
kancelář:
A1043
telefon:
+420 95155 2506
e-mail:
oldrich.semerak@matfyz.cuni.cz
www:
MFF UK

Odborné zájmy

general relativity
relativistic astrophysics
black-hole space-times

Vyučované předměty

Nabídka závěrečných prací

Vypsané a  vedené práce v SISu

Studenti

Bakalářští studenti

Magisterští studenti

Doktorští studenti

Text k předmětu Specialni TEORIE RELATIVITY:

STR.pdf

POZNÁMKY:

  • Text pokrývá víceméně přesně látku vyučovanou v kursu Speciální teorie relativity (NOFY023).
  • Omlouvám se, že stále chybějí obrázky, snad brzy doplním...

 

Lecture notes to GENERAL THEORY OF RELATIVITY, RELATIVISTIC PHYSICS I and RELATIVISTIC PHYSICS II:

GTR.pdf

REMARX:

  • Notes cover the first two semesters of GR (Obecná teorie relativity, NTMF111; and Relativistická fyzika I, NTMF037) and some topics of the third semester (Relativistická fyzika II, NTMF038). They do not (yet) include most of the topics usually covered by student talks. Will try to also add these gradually.
    Text has not "suffered" any serious check, so will be grateful for corrections, suggestions...
    Some references to other sections are not working (?? being displayed) -- it is typically because the respective sections do not yet exist.
    Bibliography is by far not complete, it has been included in an opportune way.
    Figures 2.1 and 6.2 are slightly misplaced; have been fighting with that without success. Apparently bounding box (they are eps) is not recognized correctly (though it IS there and correct).
  • 5th November 2020: Section 13.7.1 and Reissner-Nordström added.
  • 16th November: Kerr and "More on motion in black-hole fields" chapters added, together with Appendix B.
    • 18th November: Section 17.2.7 added, plus a few corrections.
  • 4th January 2021: Chapter on Black holes & gravitational collapse added (see Fig. 18.2 on energy extraction employing a perfect Bosch dynamo!), plus part of the chapter on Relativistic stellar models (as far as the TOV equation). Beware, I changed notation for the Killing vector fields in stationary and axisymmetric space-times: instead of "eta" and "xi", am now denoting them "t" and "phi" (with respective index) -- hope it is suggestive.
  • 11th January: Chapter on Relativistic stellar models written as far as Equation for energy transfer (still missing is the section on Radial oscillations).
    I have changed notation for cyclic permutation of indices from the cumbersome [...]cycl to {...}. It is described in Preface / notation part.
  • 1st February: Chapter on Relativistic stellar models finished, and chapters on Final stages of stellar evolution and on Lagrangian formulation added. Therefore, all lectures of the first two GR semesters have been covered.
    Besides that, short (but important) section 7.6 has been added, also something at the end of A.1.1. And hope you will like new figures (e.g. in Preface).
    Thanks go to Matěj Mezera for several corrections.
  • 23rd February: Chapter on Fermi-Walker transport added (applications are not compulsory; may use them next semester for seminar), plus several minor corrections.
    Thanks to Jan Střeleček and Richard Ivánek for corrections.
  • 15th March: Chapters 23 (Vector fields and their integral congruences) and 24 (3+1 splitting of space-time) added. Plus minor corrections throughout.
    Thanks to Valerie Tynianski for noticing a mistake.
  • 18th March: correcting misprints in the chapter on geodesics (thanks to Jonáš Dujava).
  • 25th March: Chapter 25 (Hamiltonian formalism in GR) included, and section on surface term in Chapter 22 (Lagrangian formalism) added. New figure 24.1 in the (3+1)-splitting Chapter.
  • 6th April: Chapter on Linearised theory and gravitational waves added (now it is Chapter 22), with its last (-but-one possibly) section yet to be done. Plus occassional editing at various places.
  • 12th April: Chapter on Linearised theory and gravitational waves continued, just would like to finish its "Gravitoelectromagnetism" section. Thanking again Matěj Mezera for several corrections.
  • 19th April: Chapter on Linearised theory and gravitational waves finished.
  • 23rd April: Section 23.1 (Action and the functional derivative) added and, at the beginning of Chapter 26 (Hamiltonian formulation), the generic name for configuration variables (fields) changed from "q" to "psi", in order to be consistent with Section 23.1.
  • 7th May: Many minor modifications, plus Kandinsky ("Weighing down", featuring the "=" sign) added after the Einstein equations. Thanks to Jonáš Dujava for comments.
  • 11th May: Section on Shapiro time delay added after apsidal advance and light bending. And paragraph on principal null directions (17.3.7) modified in normalization of the principal fields. (Thanks to Valerie Tynianski for discussion and checking.)
  • 25th May: Have simplified derivation in the Frobenius-theorem section, and also (thanks to Jonáš Dujava) "proof" of the planarity of geodesic motion in Schwarzschild.
  • 2nd June: Algebraic classification of tensor fields started. Plus minor corrections elsewhere (mainly in the Frobenius-theorem section).
  • 11th October: Several corrections at various places, mainly due to Jonáš Dujava.
  • 7th January 2022: Algebraic classification continued (Goldberg-Sachs theorem still remains to be proven), "Palatini's" variational method (hopefully) treated in a simpler way, certain extension in the null-congruence section. Plus various minor corrections -- thanks go mainly to Róbert Jurčík. "Bez názvu" by Václav Boštík added at the end by obvious reason.
  • 14th February 2022: Edit in "Effect of gravitational waves on test particles" section, thanks to Michael Vávra.
  • 31st March 2022: Minor error corrected in "d'Alembert gamma_{0j}" equation above eq. (22.37) (and, consequently, in 22.37 itself) in the Gravitoelectromagnetism section, thanks to Šimon Pajger. Plus minor edit in the Newtonian limit of Einstein equations. Plus still fighting with (simple proof of) the Goldberg-Sachs theorem... (standardly it is being proved in Newman-Penrose formalism, which I however do not want to employ).
  • 8th May 2022: Several corrections of minor mistakes, otherwise nothing new.
  • 31st October 2022: Several corrections of minor mistakes, nothing really new.
  • 23rd December 2022: Minor corrections, somewhat more concise "Palatini's variational method".
  • 20th January 2023: "Palatini's variational method" improved even more thanks to Jonáš Dujava.
  • 4th April 2023: There are always mistakes to correct...
  • 12th October 2023: Several improvements thanks to Marek Milička.
  • 21st November 2023: Few corrections thanks to Karel Balej. A short paragraph on acceleration of circular motion (specifically on the "repulsive" effect at the very centre) in Kerr added. The (summer) long list of comments from Jonáš Dujava still to be tackled...
  • 18th March 2024: Quite some changes: new chapter on Conservation laws added. (Note: still certain details on Lie derivative should be fixed, also in the Lie-derivative chapter. -Thanks to Pavel Krtouš for discussions.) Part of a new chapter on Initial (Cauchy) problem added (GR case still to be covered). And, few corrections thanks to Viktor Vařeka (mainly on Carter observers, in the Kerr section).
  • 25th March 2024: Cauchy problem for GR finished, just a "summarizing theorem" yet to be added.
  • 15th April 2024: Various improvements in the Conservation-laws chapter (also adjusting signs in definitions to match the rest of the notes), the "Pseudotensor" section yet to be done. Cauchy problem for GR finished completely.
  • 30th April 2024: Various improvements in the Conservation-laws chapter (the section on Landau-Lifshitz pseudotensor rewritten), several changes in the Hamiltonian-formalism chapter. Some additions to the chapter on Lie derivative (Lie derivative of the affine connection etc.) A short section on Geometrical objects added to the chapter on fundamental principles.
  • 14th May 2024: Slight improvements mainly in chapters on Hamiltonian formalism and Algebraic classification. Heroic section 28.2.5. corrected and completed!
  • 21st May 2024: Slight additions in the Algebraic classification chapter.
  • 29th November 2024: VERY helpful remarks by Jonáš Dujava "implemented", at last! Plus a few minor improvements.
  • 9th December 2024: Another incredible progress: hyperreferences. Have had to delete all the maths in section titles, now it should work. Enjoy :-)
  • 3rd February 2025: Again incredible: the Goldberg-Sachs theorem proved at last! Who invents shorter way will be punished somehow. (Just being obstinate, the whole chapter on algebraic classification is not in fact covered within the course.) And thanks to Karel Kraus, David Podrápský and mainly Marek Milička for comments.
  • 25rd February 2025: Many minor changes, I think useful at times.
  • 16th April 2025: Have quite rewritten (and still rewriting) the chapter on Conservation laws. (Also minor changes in the 3+1 splitting and in Hamiltonian formalism.) Am grateful to the current course audience for comments, especially Marek, Josef and Vendelín.
  • 22nd April 2025: First, Section 28.10 rewritten without using the Lie derivative of affine connection (have shifted all this stuff to 11.3.3, together with some new efforts). Second, in Chapter 23 (on Lagrangian formulation of Einstein equations), I have re-denoted all the variations as the ``barred'' ones (\bar\delta), taken ``at the same x'', consistently with the notation used in Chapter 28 on conservation laws. Third, Section 28.10.1 has been somewhat rewritten.
  • 14th May 2025: Chapter 29 on relativistic strings added, not yet complete.
  • 2nd July 2025: Chapter 29 on relativistic strings kind of completed. Lead by Brandon Carter's arXiv notes, I added the ``geometrical'' part where the main result is that the equations of motion can be written elegantly as the vanishing of the mean-curvature vector of the world-sheet.
  • 7th July 2025: Encouraged by Josef Trojan, I have supplemented the chapter on Hamiltonian formalism by sections 27.2.5 and 27.2.6 on boundary part of the Hamiltonian and ADM integral quantities.
  • 4th August 2025: Chapter 29 on strings improved, mainly in the 2+2 view of the world-sheet. Grateful to Jan Hrubeš for comments.
  • 20th August 2025: Section on Israel's junction conditions added to the chapter on 3+1 decomposition. The light-like version may also be provided in future, and some examples.
  • 26th August 2025: Junction conditions on null hypersurfaces added (Section 25.7.3).
  • 28th August 2025: In junction conditions, example of the Oppenheimer-Snyder collapse added. Looking forward to 666 pages of the file.

 

Notes on black-hole Killing horizons (part of BLACK-HOLE THERMODYNAMICS course in 2025):

Literatura

Librtfy
ORCID
Google Scholar
Research Gate
ResearcherID (WoS)

Seznam publikací s afiliací ÚTF

  1. Kotlařík, P.; Kofroň, D.; Semerák, O.: Static Thin Disks with Power-law Density Profiles ApJ 931 (2022) DOI
  2. Bičák, J.; Kofroň, D.; Semerák, O.: Trojí vzpomínání na Jiřího Langera Czech. J. Phys. 70 (2020)
  3. Semerák, O.; Čížek, P.: Rotating Disc around a Schwarzschild Black Hole Universe 6 (2020) DOI
  4. Huré, J.-M.; Basillais, B.; Karas, V.; Trova, A.; Semerák, O.: The exterior gravitational potential of toroids Mon. Not. R. Astron. Soc. 494 (2020) DOI
  5. Polcar, L.; Suková, P.; Semerák, O.: Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V ApJ 877 (2019) DOI
  6. Semerák, O.; Basovník, M.; Kotlařík, P.: Schwarzschild binary supported by an Appell ring Phys. Rev. D  99 (2019) DOI
  7. Polcar, L.; Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method Phys. Rev. D  100 (2019) DOI
  8. Kotlařík, P.; Semerák, O.; Čížek, P.: Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution Phys. Rev. D  97 (2018) DOI
  9. Costa, L. F. O.; Lukes-Gerakopoulos, G.; Semerák, O.: Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition Phys. Rev. D  97 (2018) DOI
  10. Čížek, P.; Semerák, O.: Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk ApJS 232 (2017) DOI
  11. Semerák, O.; Basovník, M.: Geometry of deformed black holes. I. Majumdar-Papapetrou binary Phys. Rev. D  94 (2016) DOI
  12. Basovník, M.; Semerák, O.: Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring Phys. Rev. D  94 (2016) DOI
  13. Semerák, O.: Static axisymmetric rings in general relativity: How diverse they are Phys. Rev. D  94 (2016) DOI
  14. Semerák, O.: Approximating Light Rays in the Schwarzschild Field ApJ 800 (2015) DOI
  15. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Particles under radiation thrust in Schwarzschild space–time from a flux perpendicular to the equatorial plane Mon. Not. R. Astron. Soc. 446 (2015) DOI
  16. Witzany, V.; Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – IV Mon. Not. R. Astron. Soc. 451 (2015) DOI
  17. Semerák, O.: Albert Einstein a století obecné relativity Pokroky Mat. Fyz. Astron. 60 (2015)
  18. Semerák, O.; Šrámek, M.: Spinning particles in vacuum spacetimes of different curvature types Phys. Rev. D  92 (2015) DOI
  19. Semerák, O.: Spinning particles in vacuum spacetimes of different curvature types: Natural reference tetrads and massless particles Phys. Rev. D  92 (2015) DOI
  20. Suková, P.; Semerák, O.: Free motion around black holes with discs or rings: between integrability and chaos – III Mon. Not. R. Astron. Soc. 436 (2013) DOI
  21. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – II Mon. Not. R. Astron. Soc. 425 (2012) DOI
  22. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.; Stella, L.: The general relativistic Poynting–Robertson effect: II. A photon flux with nonzero angular momentum Class. Quantum Grav. 28 (2011) DOI
  23. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Effect of radiation flux on test-particle motion in the Vaidya spacetime Class. Quantum Grav. 28 (2011) DOI
  24. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability Mon. Not. R. Astron. Soc. 404 (2010) DOI
  25. Kyrian, K.; Semerák, O.: Spinning test particles in a Kerr field - II Mon. Not. R. Astron. Soc. 382 (2007) DOI
  26. Šácha, J.; Semerák, O.: Toroidal source around a static black hole Czech. J. Phys. 55 (2005) DOI
  27. Semerák, O.: Albert Einstein a století moderní fyziky Pokroky Mat. Fyz. Astron. 50 (2005)
  28. Semerák, O.: Exact power-law discs around static black holes Class. Quantum Grav. 21 (2004) DOI
  29. Karas, V.; Huré, J.-M.; Semerák, O.: TOPICAL REVIEW: Gravitating discs around black holes Class. Quantum Grav. 21 (2004) DOI
  30. Semerák, O.: Gravitating discs around a Schwarzschild black hole: III Class. Quantum Grav. 20 (2003) DOI
  31. Semerák, O.: Expulsion of external fields from extreme horizons: Example of an external gravitational field Czech. J. Phys. 52 (2002) DOI
  32. Žáček, M.; Semerák, O.: Gravitating discs around a Schwarzschild black hole II Czech. J. Phys. 52 (2002) DOI
  33. Semerák, O.: Thin disc around a rotating black hole, but with support in-between Class. Quantum Grav. 19 (2002) DOI
  34. Semerák, O.; Zellerin, T.; Žáček, M.: Erratum: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 322 (2001) DOI
  35. Semerák, O.: Curvature singularity around first Morgan-Morgan disc Class. Quantum Grav. 18 (2001) DOI
  36. Semerák, O.; Žáček, M.: Gravitating discs around a Schwarzschild black hole: I Class. Quantum Grav. 17 (2000) DOI
  37. Zellerin, T.; Semerák, O.: Two-soliton stationary axisymmetric sprouts from Weyl seeds Class. Quantum Grav. 17 (2000) DOI
  38. Semerák, O.; Žáček, M.: Oscillations of Static Discs around Schwarzschild Black Holes: Effect of Self-Gravitation Publ. Astron. Soc. Jpn. 52 (2000) DOI
  39. Semerák, O.; Karas, V.: Pseudo-Newtonian models of a rotating black hole field A&A 343 (1999)
  40. Semerák, O.; Zellerin, T.; Žáček, M.: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  41. Semerák, O.; Žáček, M.; Zellerin, T.: Test-particle motion in superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  42. Semerák, O.: Spinning test particles in a Kerr field - I Mon. Not. R. Astron. Soc. 308 (1999) DOI
  43. Semerák, O.; Karas, V.; de Felice, F.: Parameters of Black Holes in Sources with Periodic Variability Publ. Astron. Soc. Jpn. 51 (1999) DOI
  44. Semerák, O.: COMMENT: Gravitomagnetic clock effect and extremely accelerated observers Class. Quantum Grav. 16 (1999) DOI
  45. Semerák, O.: Rotospheres in Stationary Axisymmetric Spacetimes Ann. Phys. 263 (1998) DOI
  46. Semerák, O.: Circular Orbits in Stationary Axisymmetric Spacetimes Gen. Relativ. Gravit. 30 (1998) DOI
  47. Semerák, O.; Bičák, J.: The interplay between forces in the Kerr-Newman field. Class. Quantum Grav. 14 (1997)
  48. Semerák, O.: Forces at the Kerr singularity Ap&SS 250 (1997) DOI
  49. Semerák, O.: Gyroscope on Polar Orbit in the Kerr Field Gen. Relativ. Gravit. 29 (1997) DOI
  50. Semerák, O.; de Felice, F.: Quasi-local measurements and orientation in black-hole fields Class. Quantum Grav. 14 (1997) DOI
  51. Semerák, O.: Collimation (and Other) Effects of the Kerr Field: an Interpretation Astrophys. Lett. Commun. 33 (1996)
  52. Semerák, O.: Photon escape cones in the Kerr field Helv. Phys. Acta 69 (1996)
  53. Semerák, O.: Extremally Accelerated Observers in Stationary Axisymmetric Spacetimes Gen. Relativ. Gravit. 28 (1996) DOI
  54. Semerák, O.: What forces act in relativistic gyroscope precession? Class. Quantum Grav. 13 (1996) DOI
  55. Semerák, O.: Some aspects of motion in the Kerr field Czech. J. Phys. 45 (1995) DOI
  56. Semerák, O.: What forces drive the relativistic motion? Nuovo Cim. B  110 (1995) DOI
  57. Semerák, O.: On the occurrence of rotospheres in the Kerr field Phys. Scr. 52 (1995) DOI
  58. Semerák, O.: On the competition of forces in the Kerr field A&A 291 (1994)
  59. Bičák, J.; Semerák, O.; Hadrava, P.: Collimation Effects of the Kerr Field Mon. Not. R. Astron. Soc. 263 (1993) DOI
  60. Semerák, O.: Stationary frames in the Kerr field Gen. Relativ. Gravit. 25 (1993) DOI
doc. RNDr. Oldřich Semerák, Ph.D., DSc.
adresa:
Ústav teoretické fyziky
Matematicko-fyzikální fakulta Univerzity Karlovy
V Holešovičkách 2
180 00 Praha 8
kancelář:
A1043
telefon:
+420 95155 2506
e-mail:
oldrich.semerak@matfyz.cuni.cz
www:
MFF UK

Odborné zájmy

general relativity
relativistic astrophysics
black-hole space-times

Vyučované předměty

Nabídka závěrečných prací

Vypsané a  vedené práce v SISu

Studenti

Bakalářští studenti

Magisterští studenti

Doktorští studenti

Text k předmětu Specialni TEORIE RELATIVITY:

STR.pdf

POZNÁMKY:

  • Text pokrývá víceméně přesně látku vyučovanou v kursu Speciální teorie relativity (NOFY023).
  • Omlouvám se, že stále chybějí obrázky, snad brzy doplním...

 

Lecture notes to GENERAL THEORY OF RELATIVITY, RELATIVISTIC PHYSICS I and RELATIVISTIC PHYSICS II:

GTR.pdf

REMARX:

  • Notes cover the first two semesters of GR (Obecná teorie relativity, NTMF111; and Relativistická fyzika I, NTMF037) and some topics of the third semester (Relativistická fyzika II, NTMF038). They do not (yet) include most of the topics usually covered by student talks. Will try to also add these gradually.
    Text has not "suffered" any serious check, so will be grateful for corrections, suggestions...
    Some references to other sections are not working (?? being displayed) -- it is typically because the respective sections do not yet exist.
    Bibliography is by far not complete, it has been included in an opportune way.
    Figures 2.1 and 6.2 are slightly misplaced; have been fighting with that without success. Apparently bounding box (they are eps) is not recognized correctly (though it IS there and correct).
  • 5th November 2020: Section 13.7.1 and Reissner-Nordström added.
  • 16th November: Kerr and "More on motion in black-hole fields" chapters added, together with Appendix B.
    • 18th November: Section 17.2.7 added, plus a few corrections.
  • 4th January 2021: Chapter on Black holes & gravitational collapse added (see Fig. 18.2 on energy extraction employing a perfect Bosch dynamo!), plus part of the chapter on Relativistic stellar models (as far as the TOV equation). Beware, I changed notation for the Killing vector fields in stationary and axisymmetric space-times: instead of "eta" and "xi", am now denoting them "t" and "phi" (with respective index) -- hope it is suggestive.
  • 11th January: Chapter on Relativistic stellar models written as far as Equation for energy transfer (still missing is the section on Radial oscillations).
    I have changed notation for cyclic permutation of indices from the cumbersome [...]cycl to {...}. It is described in Preface / notation part.
  • 1st February: Chapter on Relativistic stellar models finished, and chapters on Final stages of stellar evolution and on Lagrangian formulation added. Therefore, all lectures of the first two GR semesters have been covered.
    Besides that, short (but important) section 7.6 has been added, also something at the end of A.1.1. And hope you will like new figures (e.g. in Preface).
    Thanks go to Matěj Mezera for several corrections.
  • 23rd February: Chapter on Fermi-Walker transport added (applications are not compulsory; may use them next semester for seminar), plus several minor corrections.
    Thanks to Jan Střeleček and Richard Ivánek for corrections.
  • 15th March: Chapters 23 (Vector fields and their integral congruences) and 24 (3+1 splitting of space-time) added. Plus minor corrections throughout.
    Thanks to Valerie Tynianski for noticing a mistake.
  • 18th March: correcting misprints in the chapter on geodesics (thanks to Jonáš Dujava).
  • 25th March: Chapter 25 (Hamiltonian formalism in GR) included, and section on surface term in Chapter 22 (Lagrangian formalism) added. New figure 24.1 in the (3+1)-splitting Chapter.
  • 6th April: Chapter on Linearised theory and gravitational waves added (now it is Chapter 22), with its last (-but-one possibly) section yet to be done. Plus occassional editing at various places.
  • 12th April: Chapter on Linearised theory and gravitational waves continued, just would like to finish its "Gravitoelectromagnetism" section. Thanking again Matěj Mezera for several corrections.
  • 19th April: Chapter on Linearised theory and gravitational waves finished.
  • 23rd April: Section 23.1 (Action and the functional derivative) added and, at the beginning of Chapter 26 (Hamiltonian formulation), the generic name for configuration variables (fields) changed from "q" to "psi", in order to be consistent with Section 23.1.
  • 7th May: Many minor modifications, plus Kandinsky ("Weighing down", featuring the "=" sign) added after the Einstein equations. Thanks to Jonáš Dujava for comments.
  • 11th May: Section on Shapiro time delay added after apsidal advance and light bending. And paragraph on principal null directions (17.3.7) modified in normalization of the principal fields. (Thanks to Valerie Tynianski for discussion and checking.)
  • 25th May: Have simplified derivation in the Frobenius-theorem section, and also (thanks to Jonáš Dujava) "proof" of the planarity of geodesic motion in Schwarzschild.
  • 2nd June: Algebraic classification of tensor fields started. Plus minor corrections elsewhere (mainly in the Frobenius-theorem section).
  • 11th October: Several corrections at various places, mainly due to Jonáš Dujava.
  • 7th January 2022: Algebraic classification continued (Goldberg-Sachs theorem still remains to be proven), "Palatini's" variational method (hopefully) treated in a simpler way, certain extension in the null-congruence section. Plus various minor corrections -- thanks go mainly to Róbert Jurčík. "Bez názvu" by Václav Boštík added at the end by obvious reason.
  • 14th February 2022: Edit in "Effect of gravitational waves on test particles" section, thanks to Michael Vávra.
  • 31st March 2022: Minor error corrected in "d'Alembert gamma_{0j}" equation above eq. (22.37) (and, consequently, in 22.37 itself) in the Gravitoelectromagnetism section, thanks to Šimon Pajger. Plus minor edit in the Newtonian limit of Einstein equations. Plus still fighting with (simple proof of) the Goldberg-Sachs theorem... (standardly it is being proved in Newman-Penrose formalism, which I however do not want to employ).
  • 8th May 2022: Several corrections of minor mistakes, otherwise nothing new.
  • 31st October 2022: Several corrections of minor mistakes, nothing really new.
  • 23rd December 2022: Minor corrections, somewhat more concise "Palatini's variational method".
  • 20th January 2023: "Palatini's variational method" improved even more thanks to Jonáš Dujava.
  • 4th April 2023: There are always mistakes to correct...
  • 12th October 2023: Several improvements thanks to Marek Milička.
  • 21st November 2023: Few corrections thanks to Karel Balej. A short paragraph on acceleration of circular motion (specifically on the "repulsive" effect at the very centre) in Kerr added. The (summer) long list of comments from Jonáš Dujava still to be tackled...
  • 18th March 2024: Quite some changes: new chapter on Conservation laws added. (Note: still certain details on Lie derivative should be fixed, also in the Lie-derivative chapter. -Thanks to Pavel Krtouš for discussions.) Part of a new chapter on Initial (Cauchy) problem added (GR case still to be covered). And, few corrections thanks to Viktor Vařeka (mainly on Carter observers, in the Kerr section).
  • 25th March 2024: Cauchy problem for GR finished, just a "summarizing theorem" yet to be added.
  • 15th April 2024: Various improvements in the Conservation-laws chapter (also adjusting signs in definitions to match the rest of the notes), the "Pseudotensor" section yet to be done. Cauchy problem for GR finished completely.
  • 30th April 2024: Various improvements in the Conservation-laws chapter (the section on Landau-Lifshitz pseudotensor rewritten), several changes in the Hamiltonian-formalism chapter. Some additions to the chapter on Lie derivative (Lie derivative of the affine connection etc.) A short section on Geometrical objects added to the chapter on fundamental principles.
  • 14th May 2024: Slight improvements mainly in chapters on Hamiltonian formalism and Algebraic classification. Heroic section 28.2.5. corrected and completed!
  • 21st May 2024: Slight additions in the Algebraic classification chapter.
  • 29th November 2024: VERY helpful remarks by Jonáš Dujava "implemented", at last! Plus a few minor improvements.
  • 9th December 2024: Another incredible progress: hyperreferences. Have had to delete all the maths in section titles, now it should work. Enjoy :-)
  • 3rd February 2025: Again incredible: the Goldberg-Sachs theorem proved at last! Who invents shorter way will be punished somehow. (Just being obstinate, the whole chapter on algebraic classification is not in fact covered within the course.) And thanks to Karel Kraus, David Podrápský and mainly Marek Milička for comments.
  • 25rd February 2025: Many minor changes, I think useful at times.
  • 16th April 2025: Have quite rewritten (and still rewriting) the chapter on Conservation laws. (Also minor changes in the 3+1 splitting and in Hamiltonian formalism.) Am grateful to the current course audience for comments, especially Marek, Josef and Vendelín.
  • 22nd April 2025: First, Section 28.10 rewritten without using the Lie derivative of affine connection (have shifted all this stuff to 11.3.3, together with some new efforts). Second, in Chapter 23 (on Lagrangian formulation of Einstein equations), I have re-denoted all the variations as the ``barred'' ones (\bar\delta), taken ``at the same x'', consistently with the notation used in Chapter 28 on conservation laws. Third, Section 28.10.1 has been somewhat rewritten.
  • 14th May 2025: Chapter 29 on relativistic strings added, not yet complete.
  • 2nd July 2025: Chapter 29 on relativistic strings kind of completed. Lead by Brandon Carter's arXiv notes, I added the ``geometrical'' part where the main result is that the equations of motion can be written elegantly as the vanishing of the mean-curvature vector of the world-sheet.
  • 7th July 2025: Encouraged by Josef Trojan, I have supplemented the chapter on Hamiltonian formalism by sections 27.2.5 and 27.2.6 on boundary part of the Hamiltonian and ADM integral quantities.
  • 4th August 2025: Chapter 29 on strings improved, mainly in the 2+2 view of the world-sheet. Grateful to Jan Hrubeš for comments.
  • 20th August 2025: Section on Israel's junction conditions added to the chapter on 3+1 decomposition. The light-like version may also be provided in future, and some examples.
  • 26th August 2025: Junction conditions on null hypersurfaces added (Section 25.7.3).
  • 28th August 2025: In junction conditions, example of the Oppenheimer-Snyder collapse added. Looking forward to 666 pages of the file.

 

Notes on black-hole Killing horizons (part of BLACK-HOLE THERMODYNAMICS course in 2025):

Literatura

Librtfy
ORCID
Google Scholar
Research Gate
ResearcherID (WoS)

Seznam publikací s afiliací ÚTF

  1. Kotlařík, P.; Kofroň, D.; Semerák, O.: Static Thin Disks with Power-law Density Profiles ApJ 931 (2022) DOI
  2. Bičák, J.; Kofroň, D.; Semerák, O.: Trojí vzpomínání na Jiřího Langera Czech. J. Phys. 70 (2020)
  3. Semerák, O.; Čížek, P.: Rotating Disc around a Schwarzschild Black Hole Universe 6 (2020) DOI
  4. Huré, J.-M.; Basillais, B.; Karas, V.; Trova, A.; Semerák, O.: The exterior gravitational potential of toroids Mon. Not. R. Astron. Soc. 494 (2020) DOI
  5. Polcar, L.; Suková, P.; Semerák, O.: Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V ApJ 877 (2019) DOI
  6. Semerák, O.; Basovník, M.; Kotlařík, P.: Schwarzschild binary supported by an Appell ring Phys. Rev. D  99 (2019) DOI
  7. Polcar, L.; Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method Phys. Rev. D  100 (2019) DOI
  8. Kotlařík, P.; Semerák, O.; Čížek, P.: Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution Phys. Rev. D  97 (2018) DOI
  9. Costa, L. F. O.; Lukes-Gerakopoulos, G.; Semerák, O.: Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition Phys. Rev. D  97 (2018) DOI
  10. Čížek, P.; Semerák, O.: Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk ApJS 232 (2017) DOI
  11. Semerák, O.; Basovník, M.: Geometry of deformed black holes. I. Majumdar-Papapetrou binary Phys. Rev. D  94 (2016) DOI
  12. Basovník, M.; Semerák, O.: Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring Phys. Rev. D  94 (2016) DOI
  13. Semerák, O.: Static axisymmetric rings in general relativity: How diverse they are Phys. Rev. D  94 (2016) DOI
  14. Semerák, O.: Approximating Light Rays in the Schwarzschild Field ApJ 800 (2015) DOI
  15. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Particles under radiation thrust in Schwarzschild space–time from a flux perpendicular to the equatorial plane Mon. Not. R. Astron. Soc. 446 (2015) DOI
  16. Witzany, V.; Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – IV Mon. Not. R. Astron. Soc. 451 (2015) DOI
  17. Semerák, O.: Albert Einstein a století obecné relativity Pokroky Mat. Fyz. Astron. 60 (2015)
  18. Semerák, O.; Šrámek, M.: Spinning particles in vacuum spacetimes of different curvature types Phys. Rev. D  92 (2015) DOI
  19. Semerák, O.: Spinning particles in vacuum spacetimes of different curvature types: Natural reference tetrads and massless particles Phys. Rev. D  92 (2015) DOI
  20. Suková, P.; Semerák, O.: Free motion around black holes with discs or rings: between integrability and chaos – III Mon. Not. R. Astron. Soc. 436 (2013) DOI
  21. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability and chaos – II Mon. Not. R. Astron. Soc. 425 (2012) DOI
  22. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.; Stella, L.: The general relativistic Poynting–Robertson effect: II. A photon flux with nonzero angular momentum Class. Quantum Grav. 28 (2011) DOI
  23. Bini, D.; Geralico, A.; Jantzen, R. T.; Semerák, O.: Effect of radiation flux on test-particle motion in the Vaidya spacetime Class. Quantum Grav. 28 (2011) DOI
  24. Semerák, O.; Suková, P.: Free motion around black holes with discs or rings: between integrability Mon. Not. R. Astron. Soc. 404 (2010) DOI
  25. Kyrian, K.; Semerák, O.: Spinning test particles in a Kerr field - II Mon. Not. R. Astron. Soc. 382 (2007) DOI
  26. Šácha, J.; Semerák, O.: Toroidal source around a static black hole Czech. J. Phys. 55 (2005) DOI
  27. Semerák, O.: Albert Einstein a století moderní fyziky Pokroky Mat. Fyz. Astron. 50 (2005)
  28. Semerák, O.: Exact power-law discs around static black holes Class. Quantum Grav. 21 (2004) DOI
  29. Karas, V.; Huré, J.-M.; Semerák, O.: TOPICAL REVIEW: Gravitating discs around black holes Class. Quantum Grav. 21 (2004) DOI
  30. Semerák, O.: Gravitating discs around a Schwarzschild black hole: III Class. Quantum Grav. 20 (2003) DOI
  31. Semerák, O.: Expulsion of external fields from extreme horizons: Example of an external gravitational field Czech. J. Phys. 52 (2002) DOI
  32. Žáček, M.; Semerák, O.: Gravitating discs around a Schwarzschild black hole II Czech. J. Phys. 52 (2002) DOI
  33. Semerák, O.: Thin disc around a rotating black hole, but with support in-between Class. Quantum Grav. 19 (2002) DOI
  34. Semerák, O.; Zellerin, T.; Žáček, M.: Erratum: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 322 (2001) DOI
  35. Semerák, O.: Curvature singularity around first Morgan-Morgan disc Class. Quantum Grav. 18 (2001) DOI
  36. Semerák, O.; Žáček, M.: Gravitating discs around a Schwarzschild black hole: I Class. Quantum Grav. 17 (2000) DOI
  37. Zellerin, T.; Semerák, O.: Two-soliton stationary axisymmetric sprouts from Weyl seeds Class. Quantum Grav. 17 (2000) DOI
  38. Semerák, O.; Žáček, M.: Oscillations of Static Discs around Schwarzschild Black Holes: Effect of Self-Gravitation Publ. Astron. Soc. Jpn. 52 (2000) DOI
  39. Semerák, O.; Karas, V.: Pseudo-Newtonian models of a rotating black hole field A&A 343 (1999)
  40. Semerák, O.; Zellerin, T.; Žáček, M.: The structure of superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  41. Semerák, O.; Žáček, M.; Zellerin, T.: Test-particle motion in superposed Weyl fields Mon. Not. R. Astron. Soc. 308 (1999) DOI
  42. Semerák, O.: Spinning test particles in a Kerr field - I Mon. Not. R. Astron. Soc. 308 (1999) DOI
  43. Semerák, O.; Karas, V.; de Felice, F.: Parameters of Black Holes in Sources with Periodic Variability Publ. Astron. Soc. Jpn. 51 (1999) DOI
  44. Semerák, O.: COMMENT: Gravitomagnetic clock effect and extremely accelerated observers Class. Quantum Grav. 16 (1999) DOI
  45. Semerák, O.: Rotospheres in Stationary Axisymmetric Spacetimes Ann. Phys. 263 (1998) DOI
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  48. Semerák, O.: Forces at the Kerr singularity Ap&SS 250 (1997) DOI
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  50. Semerák, O.; de Felice, F.: Quasi-local measurements and orientation in black-hole fields Class. Quantum Grav. 14 (1997) DOI
  51. Semerák, O.: Collimation (and Other) Effects of the Kerr Field: an Interpretation Astrophys. Lett. Commun. 33 (1996)
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  54. Semerák, O.: What forces act in relativistic gyroscope precession? Class. Quantum Grav. 13 (1996) DOI
  55. Semerák, O.: Some aspects of motion in the Kerr field Czech. J. Phys. 45 (1995) DOI
  56. Semerák, O.: What forces drive the relativistic motion? Nuovo Cim. B  110 (1995) DOI
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  58. Semerák, O.: On the competition of forces in the Kerr field A&A 291 (1994)
  59. Bičák, J.; Semerák, O.; Hadrava, P.: Collimation Effects of the Kerr Field Mon. Not. R. Astron. Soc. 263 (1993) DOI
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