Stability issues of black hole in non-local gravity

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 γ 2 = −2γ 0 cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with γ 2 = 0, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with γ 2 = −2γ 0 = const (fourthorder 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.

Black-hole stability in non-local gravity

“…The case of black holes is especially interesting because, currently, there are three different views: black holes in nonlocal gravity may form but are singular [6,7], they form and are regular [8][9][10][11][12][13][14][15], or they may not even form as asymptotic, classically stable states [16,17]. The first view is the subject of the present paper (we will comment about the second view in the concluding section).…”

Non-perturbative spectrum of non-local gravity

“…Selecting the gauge-independent terms of the action, we get (30) Notice that the local limit of the form factors in (30) is…”

“…Causality is not violated in the usual eikonal limit [16] and one expects nonoffensive microcausality violations at the non-locality scale. The Email addresses: g.calcagni@csic.es (Gianluca Calcagni), lmodesto@sustc.edu.cn (Leonardo Modesto), giuseppe.nardelli@unicatt.it (Giuseppe Nardelli) theory may resolve the big bang [17][18][19][20][21][22][23][24][25] and black-hole singularities [26][27][28][29][30][31], and its cosmological solutions may unravel interesting bottom-up scenarios in the early universe (inflation) and at late times (dark energy). Surprisingly, these encouraging features are accompanied by a number of appalling gaps of knowledge on basic questions on the classical theory, such as how to find solutions of the dynamics and whether they match the singularity-free geometries found when linearizing the equations of motion.…”

“…Causality is not violated in the usual eikonal limit [16] and one expects nonoffensive microcausality violations at the non-locality scale. The theory may resolve the big bang [17][18][19][20][21][22][23][24][25] and black-hole singularities [26][27][28][29][30][31], and its cosmological solutions may unravel interesting bottom-up scenarios in the early universe (inflation) and at late times (dark energy).…”

Stability of Kerr black holes in generalized hybrid metric-Palatini gravity

“…The analysis was even extended to include the stability of the Schwarzschild-AdS black hole in f (R) theories with a negative cosmological constant [23] with the conclusion that stable solutions against external perturbations exist if the scalaron is again free from tachyons. The stability of the Schwarzschild black hole was also analyzed in several extensions of f (R) gravity [24][25][26]. The study of the stability of the Kerr solution in f (R) gravity has been studied in [27,28], where it has been proved that it is unstable due to the fact that the perturbation equation for the massive spin-0 graviton in this theory, or equivalently the perturbed Ricci scalar, is analogous to a Klein-Gordon equation for a massive scalar field in general relativity which has been intensively studied and showed to be unstable.…”