On the existence and dynamics of braneworld black holes

TL;DR

The paper reevaluates the existence and dynamics of large black holes localized on a brane in RS2 by emphasizing the strongly coupled holographic dual. It presents a concrete counter-example to the claim that static localized brane black holes cannot exist and argues that static solutions are not ruled out once strong coupling is properly accounted, though they may be dynamically unstable via a Gregory-Laflamme–style mechanism. It analyzes the geometry of large brane black holes and the holographic interpretation of potential instabilities, concluding that spontaneous Hawking radiation does not necessarily prevent static solutions but that non-spontaneous energetic instabilities could occur depending on bulk details. An effective theory interpretation shows that the presence of a gapless KK spectrum alters the 4D description near large black holes, making a simple 4D reduction inadequate and highlighting the need for nonperturbative 5D analysis to fully determine stability and evolution.

Abstract

Based on holographic arguments Tanaka and Emparan et al have claimed that large localized static black holes do not exist in the one-brane Randall-Sundrum model. If such black holes are time-dependent as they propose, there are potentially significant phenomenological and theoretical consequences. We revisit the issue, arguing that their reasoning does not take into account the strongly coupled nature of the holographic theory. We claim that static black holes with smooth metrics should indeed exist in these theories, and give a simple example. However, although the existence of such solutions is relevant to exact and numerical solution searches, such static solutions might be dynamically unstable, again leading to time dependence with phenomenological consequences. We explore a plausible instability, suggested by Tanaka, analogous to that of Gregory and Laflamme, but argue that there is no reliable reason at this point to assume it must exist.

Figures (2)

• Figure 1: Surfaces in AdS in $r,z$ coordinates, computed from linear theory, whose intrinsic geometry approximates the horizon geometry of black holes of 3 sizes: $4L,8L,$ and $12L$. We see these large localized black holes have horizon geometries simply related by a global scaling, and extend a coordinate distance $\Delta z \sim 2 R_S$ into the bulk.
• Figure 2: The horizon of the brane black hole from linearized gravity and the horizon of the perturbed black string. The perturbation shown is the unstable mode with the shortest wavelength.