(In)stability of black holes in the 4 D EinsteinGaussBonnet and EinsteinLovelock gravities
Abstract
A (3 + 1) dimensional EinsteinGaussBonnet effective description of gravity has been recently formulated as the D → 4 limit of the higher dimensional field equations after the rescaling of the coupling constant. This approach has been recently extended to the fourdimensional EinsteinLovelock gravity. Although validity of the regularization procedure has not been shown for the general case, but only for a wide class of metrics, the blackhole solution obtained as a result of such a regularization is also an exact solution in the well defined 4 D EinsteinGaussBonnet theory suggested by Aoki et al. (2005) and in the scalartensor effective classical theories. Here we study the eikonal gravitational instability of asymptotically flat, de Sitter and antide Sitter black holes in the four dimensional EinsteinGaussBonnet and EinsteinLovelock theories. We find parametric regions of the eikonal instability for various orders of the Lovelock gravity, values of coupling and cosmological constants, and share the code which allows one to construct the instability region for an arbitrary set of parameters. For the fourdimensional GaussBonnet black holes we obtain the region of stability in analytic form. Unlike the higher dimensional EinsteinLovelock case, the eikonal instability serves as an effective cutoff of higher curvature Lovelock terms for the 4 D black holes.
 Publication:

Physics of the Dark Universe
 Pub Date:
 December 2020
 DOI:
 10.1016/j.dark.2020.100697
 arXiv:
 arXiv:2003.12492
 Bibcode:
 2020PDU....3000697K
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 High Energy Physics  Theory
 EPrint:
 14 pages (JCAP style), 3 figures