Regular Schwarzschild-like spacetime embedded in a five dimensional bulk

TL;DR

This paper derives a new five-dimensional brane-world solution with a regular Schwarzschild-like spacetime, revealing anisotropic stresses and a black string configuration without curvature singularities.

Contribution

It introduces a novel brane solution with a specific conformal factor, expanding the understanding of bulk-brane interactions and black string geometries.

Findings

Positive energy density and negative radial pressure on the brane.

Black hole appears as a black string in 5D space.

No curvature singularities in the solution.

Abstract

We take advantage of the Shiromizu et al. covariant formalism to find out the brane properties originating from the five dimensional bulk spacetime. Making a different choice for the conformal factor $e^{-2b(z)}$ compared to Estrada [24], we reach a new solution with a lot of interesting properties, where $b(z) = ln(1/\sqrt{cosh2\mu z})$. The non-local tensor $E_{ab}$ rooted from the 5-dimensional Riemann tensor gives an anisotropic stress energy tensor on the brane with positive energy density and negative radial pressure. The BH on the brane looks like a black string in the 5-dimensional space, with no singularities of the curvature invariants.