https://doi.org/10.1140/epjc/s10052-020-08639-8
Regular Article - Theoretical Physics
Quasinormal modes, stability and shadows of a black hole in the 4D Einstein–Gauss–Bonnet gravity
1
Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, 746 01, Opava, Czech Republic
2
Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation
Received:
1
September
2020
Accepted:
3
November
2020
Published online:
12
November
2020
Recently a D-dimensional regularization approach leading to the non-trivial 
-dimensional Einstein–Gauss–Bonnet (EGB) effective description of gravity was formulated which was claimed to bypass the Lovelock’s theorem and avoid Ostrogradsky instability. Later it was shown that the regularization is possible only for some broad, but limited, class of metrics and Aoki et al. (arXiv:2005.03859) formulated a well-defined four-dimensional EGB theory, which breaks the Lorentz invariance in a theoretically consistent and observationally viable way. The black-hole solution of the first naive approach proved out to be also the exact solution of the well-defined theory. Here we calculate quasinormal modes of scalar, electromagnetic and gravitational perturbations and find the radius of shadow for spherically symmetric and asymptotically flat black holes with Gauss–Bonnet corrections. We show that the black hole is gravitationally stable when (
). The instability in the outer range is the eikonal one and it develops at high multipole numbers. The radius of the shadow 
obeys the linear law with a remarkable accuracy.
© The Author(s) 2020
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
