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

Recently [D.~Glavan and C.~Lin, Phys.\ Rev.\ Lett.\ {\bf 124}, 081301 (2020)] a non-trivial $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity was formulated which bypasses the Lovelock's theorem and avoids Ostrogradsky instability. 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 in this theory. We have shown that the damping rate is more sensitive characteristic than the real oscillation frequency: it leads to considerable deviation from the Schwarzschild limit by tens of percents. We show that the coupling constant must be relatively small in order to avoid dynamical instabilities in the gravitational sector. The radius of the shadow $R_{Sh}$ obeys the linear law $R_{Sh} \approx (3 \sqrt{3}/2) + 0.94 \alpha$ with a remarkable accuracy.