Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Localized five-dimensional rotating brane-world black hole Analytically Connected to an to an AdS$_5$ boundary

Milko Estrada, Francisco Tello-Ortiz

TL;DR

This paper presents a bulk-first construction of a $5D$ rotating braneworld black hole that is analytically localized near a four-dimensional Kerr brane and asymptotically approaches $AdS_5$. By applying the $5D$ Janis–Newman algorithm in Hopf coordinates to a warped seed metric, the authors obtain a rotating bulk whose induced brane metric is Kerr, and whose bulk energy-momentum transitions from a non-diagonal anisotropic form to a negative cosmological constant. The solution features two curvature singularities, pancake-shaped horizons that extend into the extra dimension, and an ergosurface structure that likewise extends bulk-ward, with the inner horizon disappearing faster than the outer. Energy conditions are carefully analyzed via a dual-basis diagonalization, revealing localized bulk violations essential for brane confinement, and the asymptotic bulk tends to $AdS_5$, validating the holographic-like boundary interpretation. Overall, the work provides a coherent analytic framework for a rotating, localized 5D black hole connected to an $AdS_5$ boundary, deepening understanding of bulk effects on brane Kerr spacetimes and horizon geometry in higher dimensions.

Abstract

We provide a method to describe the geometry of an analytic, exponentially localized $5D$ rotating braneworld black hole, using the $5D$ Janis Newman algorithm in Hopf coordinates. The induced metric on the brane matches the standard $4D$ Kerr spacetime. Two curvature singularities arise: one confined to the $3$-brane at $z = r = 0$, and another that, on the brane, reproduces the Kerr singularity at $r = 0$, $\barθ = π/2$. The inner and event horizons, together with the stationary limit hypersurfaces, extend into the extra dimension in a pancake-like shape. We describe their behavior in the bulk. The energy momentum tensor represents a source transitioning from an anisotropic, non diagonal structure to a vacuum with negative cosmological constant. Thus, the localized black hole connects to an AdS$_5$ boundary. The geometry is supported by a non-diagonal anisotropic fluid in the bulk, requiring no matter on the brane. To evaluate the energy conditions, we use a one form from the dual basis that yields a diagonal energy momentum tensor.

Localized five-dimensional rotating brane-world black hole Analytically Connected to an to an AdS$_5$ boundary

TL;DR

This paper presents a bulk-first construction of a rotating braneworld black hole that is analytically localized near a four-dimensional Kerr brane and asymptotically approaches . By applying the Janis–Newman algorithm in Hopf coordinates to a warped seed metric, the authors obtain a rotating bulk whose induced brane metric is Kerr, and whose bulk energy-momentum transitions from a non-diagonal anisotropic form to a negative cosmological constant. The solution features two curvature singularities, pancake-shaped horizons that extend into the extra dimension, and an ergosurface structure that likewise extends bulk-ward, with the inner horizon disappearing faster than the outer. Energy conditions are carefully analyzed via a dual-basis diagonalization, revealing localized bulk violations essential for brane confinement, and the asymptotic bulk tends to , validating the holographic-like boundary interpretation. Overall, the work provides a coherent analytic framework for a rotating, localized 5D black hole connected to an boundary, deepening understanding of bulk effects on brane Kerr spacetimes and horizon geometry in higher dimensions.

Abstract

We provide a method to describe the geometry of an analytic, exponentially localized rotating braneworld black hole, using the Janis Newman algorithm in Hopf coordinates. The induced metric on the brane matches the standard Kerr spacetime. Two curvature singularities arise: one confined to the -brane at , and another that, on the brane, reproduces the Kerr singularity at , . The inner and event horizons, together with the stationary limit hypersurfaces, extend into the extra dimension in a pancake-like shape. We describe their behavior in the bulk. The energy momentum tensor represents a source transitioning from an anisotropic, non diagonal structure to a vacuum with negative cosmological constant. Thus, the localized black hole connects to an AdS boundary. The geometry is supported by a non-diagonal anisotropic fluid in the bulk, requiring no matter on the brane. To evaluate the energy conditions, we use a one form from the dual basis that yields a diagonal energy momentum tensor.

Paper Structure

This paper contains 11 sections, 54 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Methodology Revisited
  3. The new rotating case
  4. The induced metric on the brane
  5. The energy momentum tensor on the brane
  6. Singularity of the $5D$ spacetime and asymptotic behavior
  7. Event Horizon
  8. Energy conditions
  9. Discussion and Summarize
  10. A brief overview of the Randall-Sundrum model.
  11. Components of the energy-momentum tensor

Figures (4)

  • Figure 1: brane world set up
  • Figure 2: Behavior of the horizons $r_{\pm}$ for $k=b=1,M=2.1$
  • Figure 3: Behavior of the horizons $r_{\pm}$ vs $r^{(s)}_{\pm}$ for $k=b=1,M=2.1$
  • Figure 4: Energy conditions for $b=1,k=0.25, M=2.1,r=0.2$