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

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