Quasinormal modes, stability and shadows of a black hole in the 4D Einstein–Gauss–Bonnet gravity

Abstract

Recently a D-dimensional regularization approach leading to the non-trivial $$(3+1)$$ ( 3 + 1 ) -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 ($$-16 M^2<\alpha \lessapprox 0.6 M^2$$ - 16 M 2 < α ⪅ 0.6 M 2 ). The instability in the outer range is the eikonal one and it develops at high multipole numbers. The radius of the shadow $$R_{Sh}$$ R Sh obeys the linear law with a remarkable accuracy.

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

“…Interestingly, the solution of the same form has been presented in the conformal anomaly inspired gravity [40,41]. Along this line, the Einstein-Gauss-Bonnet gravity in the 4D spacetime has been explored extensively on various aspects, including the exact solutions [42][43][44][45][46][47][48][49][50][51][52][53][54][55], the quasinormal modes and stability [56][57][58][59][60][61][62][63][64][65][66][67], the observable shadows [68][69][70][71][72][73], the geodesics and gravitational lensing [74][75][76][77][78], and the thermodynamics and cosmic censorship conjecture [79][80][81][82][83][84][85][86].…”

4D Einstein-Gauss-Bonnet gravity: Massless particles and absorption of planar spin-0 waves

“…Many properties of the spacetime (1) have been studied recently in a number of papers, for instance, in Refs. [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].…”

“…Null geodesics, gravitational lensing and shadows in the 4D-EGB BH were recently studied in Refs. [48,49,59]. Since the line element 1is spherically symmetric, we may restrict our analysis to the equatorial plane without loss of generality.…”

Ringing of rotating black holes in higher-derivative gravity

“…Calculations of QNM frequencies are rather involved, however, and have often been performed using various approximations. Recently, much progress has been reported on the calculation of QNM frequencies for spherical black holes in a broad range of modifications of GR [19][20][21][22][23][24][25] -see also [26,27] for a parametrized formalism. Coalescences of observational interest, however, typically involve black holes with significant angular momentum [1].…”