Stability issues of black hole in non-local gravity

TL;DR

This paper investigates the stability of Schwarzschild black holes within various non-local gravity theories, revealing that stability depends on the specific properties like unitarity and renormalizability of the gravity model.

Contribution

It provides a detailed stability analysis of black holes in different non-local gravity frameworks, highlighting the challenges posed by unitarity and renormalizability constraints.

Findings

Black hole stability cannot be analyzed using the Lichnerowicz operator in certain non-local gravity models.

Black holes are stable in unitary, non-renormalizable non-local gravity with specific parameter choices.

Small black holes are unstable in local, renormalizable, fourth-order gravity models.

Abstract

We discuss stability issues of Schwarzschild black hole in non-local gravity. It is shown that the stability analysis of black hole for the unitary and renormalizable non-local gravity with $\gamma_2=-2\gamma_0$ cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with $\gamma_2=0$, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with $\gamma_2=-2\gamma_0={\rm const}$ (fourth-order gravity), the small black holes are unstable against the metric perturbations. This implies that what makes the problem difficult in stability analysis of black hole is the simultaneous requirement of unitarity and renormalizability around the Minkowski spacetime.