# Black holes in higher-dimensional spacetimes

**Advisor:** Marcello Ortaggio (IM CAS)

**Funding:** Basic scholarship

**Website:** http://www.math.cas.cz/homepage/main_page.php?id_membre=58

**Contact:** ortaggio@math.cas.cz

Gravity in higher dimensions has developed into an active and interdisciplinary area of ongoing studies. It has applications in fundamental theories as well as in phenomenology. The topic of the thesis includes the analysis and construction of exact solutions of Einstein's equations in various spacetime dimensions, in particular black holes. At the start, the student will become familiar with techniques such as the Newman-Penrose and Geroch-Held-Penrose formalisms and their extensions, and with geometric methods for the classification of spacetimes. These will be subsequently employed in the research work.

Gravity in more than four spacetime dimensions is an area of active theoretical research, motivated, e.g., by fundamental theories such as string theory, along with the idea of extra dimensions and braneworld models of TeV gravity. The study of higher-dimensional Lorentzian spaces is of interest also from a purely geometrical viewpoint. Several qualitatively new higher-dimensional features have been revealed in recent years. These range from uniqueness and stability properties of black holes, to the asymptotic behavior of gravitational and electromagnetic fields and extensions of the Goldberg-Sachs theorem.

This project will aim at answering some remaining open questions about the “uniqueness” of certain (electro)vacuum black hole solutions within algebraically special spacetimes and the characterization of the space of solutions which satisfies certain boundary conditions [1-3]. Analytic techniques developed by our group and collaborators in the past few years such as the Newman-Penrose and Geroch-Held-Penrose formalisms) will be a useful tool for this investigation [4].

References:

[1] M. Ortaggio, V. Pravda, A.
Pravdová, On asymptotically flat algebraically special spacetimes in higher
dimensions, Phys. Rev. D 80, 084041 (2009).

[2] G. Bernardi de Freitas, M.
Godazgar, H. S. Reall, Uniqueness of the Kerr–de Sitter Spacetime as an
Algebraically Special Solution in Five Dimensions, Commun. Math. Phys. 340
(2015) 291-323

[3] M. Ortaggio, On the uniqueness of the Myers-Perry
spacetime as a type II(D) solution in six dimensions, JHEP 1706 (2017)
042.

[4] M. Ortaggio, V. Pravda and A. Pravdová, Algebraic classification of
higher dimensional spacetimes based on null alignment, 2013 Class. Quantum Grav.
30 013001