Exact solutions in extended theories of gravity

There are several theoretical reasons to study various modifications of Einstein gravity obtained by adding correction terms to the Einstein-Hilbert action and/or by changing the number of spacetime dimensions. The resulting field equations are usually much more involved than in the case of standard Einstein gravity. Thus these equations are naturally studied mostly numerically or using perturbative methods and only a few exact vacuum solutions to most extended gravities are known. Nevertheless similarly as in Einstein's gravity, exact solutions play an important role in the understanding of various aspects of a theory.

The goal of the project will be to study vacuum (or possibly also admitting physically motivated matter fields) solutions to selected theories of gravity, such as Lovelock gravity, quadratic gravity, and other gravities, using analytical methods. Depending on student's preferences, the focus can be on generalizing so-called universal solutions which simultaneously solve vacuum equations of a large class of modified gravities (see, e.g., [1] for details) and related solutions (see, e.g., almost universal spacetimes [2]) or on studying solutions in a specific generalized theory of gravity of interest (see e.g. [3]).

[1] Hervik, Pravda, Pravdova, JHEP 1710 (2017): 28

[2] Kuchynka, Malek, Pravda, Pravdova, Phys. Rev. D 99, 024043 (2019)

[3] Svarc, Podolsky, Pravda, Pravdova, Phys. Rev. Lett. 121, 231104 (2018)

Pravda, Pravdova, Podolsky, Svarc, Phys. Rev. D 95, 084025 (2017)