Recent research of quantum chaos in the context of the holographic duality elucidated a property of thermal Green functions now known as pole-skipping. In this thesis we investigate the gravitational implications of this phenomenon. We focus on the simplest physical type of a black hole: the Schwarzschild black hole with an arbitrary cosmological constant. In particular, in these spaces, we analyse the gravitational waves by solving the perturbed Einstein equations using spherical harmonics decomposition. In terms of the gravitational picture, the pole-skipping points signal the fact that the physical boundary condition imposed at the black hole’s event horizon fails to uniquely determine the solution of the perturbed Einstein equations. For Schwarzschild black holes, we find all such points and show that infinitely many of them exist even in the asymptotically flat case. We also classify all such points in asymptotically de Sitter and anti-de Sitter spaces and support the conclusions with numerical analysis. At last we discuss the difficulty of understanding the possible physical implications of this phenomenon.
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