Exact solutions to modified theories of gravity

Exact solutions of Einstein's equations, such as the Schwarzschild, Kerr, or gravitational wave metrics, play a crucial role in our understanding of various mathematical and physical aspects of General Relativity. The field equations of modified gravities, such as Gauss-Bonnet gravity, Lovelock gravity, quadratic gravity, etc., are generally even more challenging to solve, and very few exact solutions are known. In this project, we will search for exact solutions of modified gravities using various simplifying assumptions, such as algebraically special spacetime and/or a high degree of symmetry.

The candidate should be familiar with the most important exact solutions of Einstein's gravity and have a basic knowledge of algebraic classification and algebraically special spacetimes.

References:

[1] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein's Field Equations. Cambridge University Press, second ed., 2003.
[2] J. B. Griffiths, J. Podolsky, Exact space-times in Einstein's general relativity, Cambridge University Press, 2012.
[3] M. Ortaggio, V. Pravda, and A. Pravdová, Algebraic classification of higher-dimensional spacetimes based on null alignment, Class. Quantum Grav. 30, 013001, 2013.
[4] S. Hervik, V. Pravda, and A. Pravdová, Type III and N universal spacetimes, Class. Quantum Grav. 31, 215005, 2014.
[5] R. Švarc, J. Podolský, V. Pravda, and A. Pravdová, Exact black holes in quadratic gravity with any cosmological constant. Phys. Rev. Lett., 121:231104, 2018.
[6] M. Kuchynka, T. Málek, V. Pravda, and A. Pravdová, Almost universal spacetimes in higher-order gravity theories, Phys. Rev. D 99, 024043, 2019.