Novel black holes in higher derivative gravity

Abstract

We find a class of novel black holes in higher derivative theory. The novel black holes follow behavior of Schwarzschild ones at large mass limit, while dramatically differentiate from Schwarzschild ones for little holes because of the effects which may root in quantum gravity. The temperature of the hole takes maximum for a specific mass, which is related to the new sale introduced in the higher derivative theory, and goes to zero at little mass limit. This property leads to a significant observation that the novel black hole may be a candidate for dark matters evading constraint from γ-ray burst.

Topological black holes in higher derivative gravity

“…However, similarly as in the case of spherical horizons with = 0 [11][12][13]15,16,18,19,21], it turns out that, for generic values of the parameters a 0 and b, the metric functions h and f diverge as r → +∞. In order to remedy this one needs to fine-tune the parameter b (for any given a 0 ), such that in the weak gravity regime, one recovers a solution of general relativity.…”

“…Stemming from the early results of [9,10], recently there has been a great interest in the study of static, spherically symmetric black holes in quadratic gravity [11][12][13][14][15][16][17][18][19][20][21], where corrections quadratic in the curvature are added to the Einstein-Hilbert action…”

“…An exact solution in a closed form describing this black hole is unknown -in the = 0 case, evidence for the existence of this black hole has been provided in [11,12] by taking the first few terms in the near-horizon expansion and numerically integrating the solution out from the horizon to some point outside the horizon, before the numerical solution diverges (the fourth order equations of motion are numerically unstable). As it turns out, to ensure the asymptotic flatness of the spacetime (such as to kill the growing Yukawa modes), one needs to fine-tune the parameters r0 and b using numerical methods, thus effectively ending up with a one-parameter family of solutions [11][12][13]15,18,21]. Very recently, it has been shown that for a given r0 there exist at least two values of b giving an asymptotically flat black hole [21].…”

“…As it turns out, to ensure the asymptotic flatness of the spacetime (such as to kill the growing Yukawa modes), one needs to fine-tune the parameters r0 and b using numerical methods, thus effectively ending up with a one-parameter family of solutions [11][12][13]15,18,21]. Very recently, it has been shown that for a given r0 there exist at least two values of b giving an asymptotically flat black hole [21]. However, introducing a non-zero cosmological constant or non-spherical horizon topologies into the picture may have significant consequences on the physics of these black holes.…”

“…Interestingly, depending on and , the Einstein limit of the black hole solutions constructed here contains not only (A)dS-Schwarzschild black holes with a transverse space of arbitrary curvature, but also naked singularities, Kundt metrics of the (anti-)Nariai type -dS 2 ×S 2 , AdS 2 ×H 2 , and flat spacetime. As in the spherical case [11][12][13][15][16][17][18][19][20][21], one might expect that, by fine-tuning the Bach parameter, a quadratic-gravity black hole with = 0 will asymptote an (appropriate) Ricci-flat metric near spatial infinity. We will give evidence to support this expectation by fine-tuning a planar black-hole solution ( = 0) with vanishing , using the polynomial expansion.…”