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 γ2=−2γ0 cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with γ2=0, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with γ2=−2γ0=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.
Highlights
It turns out that the infinite derivative gravity is ghostfree and renormalizable around the Minkowski spacetime background when one chooses the exponential form of an entire function [1, 2]
In order to check that the Schwarzschild black hole exists really in the unitary and renormalizable non-local gravity, one has to perform the stability analysis of the black hole
For a unitary and non-renormalizable gravity with γ2 = 0, it has shown that the black hole is stable against the metric perturbations
Summary
It turns out that the infinite derivative gravity (non-local gravity) is ghostfree and renormalizable around the Minkowski spacetime background when one chooses the exponential form of an entire function [1, 2]. It has shown that the Schwarzschild black hole is stable against linear perturbations for a subclass of unitary non-local gravity with γ2 = 0 [8] This case is not a renormalizable gravity around Minkowski spacetime. For the non-unitary and renormalizable local gravity with γ2 = −2γ0 = const (fourth-order gravity) [10], using the Gregory-Laflamme black string instability [11], the small black holes are unstable against the Ricci tensor perturbations. This contrasts to the conventional stability analysis of black hole in Einstein gravity or f (R) gravity. It implies that the simultaneous requirement for unitarity and renormalizability makes the stability analysis difficult
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