Regular Schwarzschild-like spacetime embedded in a five dimensional bulk

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 (0000), we reach a new solution with a lot of interesting properties, where b(z)=ln(1/cosh2μz). The non-local tensor Eab 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.