Stability issues of black hole in non-local gravity

Understand

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.