Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bulk shape of brane-world black holes

Roberto Casadio, Lorenzo Mazzacurati

TL;DR

The paper tackles extending asymptotically flat brane-world black-hole metrics into the five-dimensional bulk within a Randall–Sundrum framework by employing a $1/r$ multipole expansion and exact integration along the extra dimension. A metric ansatz is combined with on-brane constraints and Israel junction conditions to derive a recursive bulk solution, enabling analysis of the bulk horizon geometry. For η<0, the authors find the bulk horizon closes into a pancake shape with a finite tip height and a horizon area scaling with $M$; this contrasts with the unstable black-string configuration and avoids the Kretschmann divergence along the axis. The approach highlights parameter dependencies and potential implications for Hawking evaporation, while also noting a qualitatively different bulk behavior for η>0 and outlining avenues for refinement and stability studies.

Abstract

We propose a method to extend into the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parameterized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat ``pancake'' for astrophysical sources.

Bulk shape of brane-world black holes

TL;DR

The paper tackles extending asymptotically flat brane-world black-hole metrics into the five-dimensional bulk within a Randall–Sundrum framework by employing a multipole expansion and exact integration along the extra dimension. A metric ansatz is combined with on-brane constraints and Israel junction conditions to derive a recursive bulk solution, enabling analysis of the bulk horizon geometry. For η<0, the authors find the bulk horizon closes into a pancake shape with a finite tip height and a horizon area scaling with ; this contrasts with the unstable black-string configuration and avoids the Kretschmann divergence along the axis. The approach highlights parameter dependencies and potential implications for Hawking evaporation, while also noting a qualitatively different bulk behavior for η>0 and outlining avenues for refinement and stability studies.

Abstract

We propose a method to extend into the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parameterized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat ``pancake'' for astrophysical sources.

Paper Structure

This paper contains 4 sections, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The procedure
  3. Application to brane-world black holes
  4. Conclusions and outlook

Figures (4)

  • Figure 1: The function $R^2_n$ near $z^{\rm axis}$ evaluated to orders $n=10\to 19$ for the data (\ref{['para']}) and $r=M$(a), $r=r_{\rm h}=2\,M$(b), and $r=3\,M$(c) (lengths are in units of $\sigma^{-1}$).
  • Figure 2: The function $R^2$ evaluated to order $n=19$ for $r=M$, $r_{\rm h}=2\,M$ (dashed line) and $10\,M$ with $M=10^6\,\sigma^{-1}$ and $\eta=-10^{-4}$.
  • Figure 3: Qualitative picture of the bulk structure.
  • Figure 4: The function $R^2/R^2_{\rm BS}$ evaluated to order $n=19$ for $r=M$, $r_{\rm h}=2\,M$ (dashed line), $10\,M$ and $100\,M$ with $M=10^7\,\sigma^{-1}$ and $\eta=-10^{-4}$.