Large Randall–Sundrum II black holes

Abstract

Using a novel numerical spectral method, we have constructed an AdS 5 -CFT 4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall-Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in 1/(−ΛM 2 ), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−Λ).

Hawking Radiation from Higher-Dimensional Black Holes

“…But there are also counter-arguments to the above [86,87,88] according to which one should not expect important quantum corrections on the brane. In support of the latter view, recent numerical studies [89,90,91] find solutions that describe both small and large black holes in the context of the RS model (see also [92,93,94,95,96]). …”

“…The numerical nature of the solutions found in [89,90,91], describing both small and large black holes in the RS-II model, does not allow us to analytically study the effect that the brane tension or the bulk cosmological constant have on the evaporation process. In the context of a six-dimensional model, a solution was found [158] that described a black hole localised on a codimension-two brane with tension.…”

Perturbative construction of stationary Randall-Sundrum II black holes on a 5-brane

“…We applied this perturbative construction to leading order to the static AdS 5 /CF T 4 solution of [11] and the stationary AdS 6 /CF T 5 solution of [12]. This perturbative approach has been employed previously in [1,2]. Using a numerical method independent of the Ricci-flow approach of [11] the authors constructed an AdS 5 /CF T 4 solution that is asymptotically conformal to the Schwarzschild metric and perturbed it to leading order.…”

Incorporating physical constraints in braneworld black-string solutions for a Minkowski brane in scalar-tensor gravity

“…However, the presence of this factor has proven to be an insurmountable obstacle in the derivation of an analytical, non-approximate solution describing a regular, localized-close-to-our-brane black hole (see Refs. for an impartial list of works on this topic; for a number of numerical solutions describing in principle regular brane-world black holes, see [47][48][49][50][51][52][53]).…”