[Paper Review] Small Black Holes in Randall-Sundrum I Scenario

David Karasik, C. Sahabandu+2 more|arXiv (Cornell University)|Sep 16, 2003

Black Holes and Theoretical Physics4 citations

TL;DR

This paper develops a perturbative approximation method to study small black holes on the TeV brane in the Randall-Sundrum I model. By expanding in the ratio of the black hole's Schwarzschild radius to the bulk curvature length, it derives a metric solution valid near the horizon, using linearized gravity as an asymptotic boundary condition up to first order, though horizon regularity remains under investigation.

ABSTRACT

An approximation method to study the properties of a small black hole located on the TeV brane in the Randall-Sundrum type I scenario is presented. The method enables us to find the form of the metric close to the matter distribution when its asymptotic form is given. The short range solution is found as an expansion in the ratio between the Schwarzschild radius of the black hole and the curvature length of the bulk. Long range properties are introduced using the linearized gravity solution as an asymptotic boundary condition. The solution is found up to first order. It is valid in the region close to the horizon but is not valid on the horizon. The regularity of the horizon is still under study.

Motivation & Objective

• To model the metric of a small black hole localized on the TeV brane in the Randall-Sundrum I scenario.
• To address the challenge of finding a consistent metric solution near the black hole horizon when the bulk curvature is significant.
• To combine short-range nonlinear solutions with long-range linearized gravity as a boundary condition.
• To provide a first-order approximation valid in the vicinity of the horizon, excluding the horizon itself.
• To lay the groundwork for analyzing horizon regularity in this higher-dimensional gravity framework.

Proposed method

• Uses a perturbative expansion in the ratio of the black hole's Schwarzschild radius to the bulk curvature length.
• Derives the short-range metric solution near the black hole using nonlinear gravity effects.
• Applies the linearized gravity solution in the bulk as an asymptotic boundary condition for the metric.
• Constructs the solution up to first order in the perturbation parameter.
• Ensures consistency between the short-range nonlinear solution and the long-range linearized behavior.
• Focuses on the region close to the horizon, excluding the horizon itself due to singular behavior.

Experimental results

Research questions

• RQ1 How can a consistent metric be constructed for a small black hole on the TeV brane in the Randall-Sundrum I model?
• RQ2 What is the behavior of the gravitational field near the black hole horizon when bulk curvature is non-negligible?
• RQ3 How can short-range nonlinear solutions be matched to long-range linearized gravity solutions?
• RQ4 What are the implications of the perturbative approach for the regularity of the black hole horizon?
• RQ5 Can a first-order solution be reliably used to study black hole properties near the horizon in this setup?

Key findings

• A first-order metric solution is successfully derived for a small black hole near the horizon in the Randall-Sundrum I scenario.
• The solution is valid in the region close to the horizon but not on the horizon itself.
• The method successfully combines nonlinear short-range effects with linearized long-range gravity via boundary conditions.
• The perturbative approach is based on the ratio of the Schwarzschild radius to the bulk curvature length, enabling systematic expansion.
• The regularity of the horizon remains an open issue, not resolved by this first-order solution.
• The framework provides a foundation for further study of black hole properties and horizon structure in warped extra dimensions.