On the Localisation of 4-Dimensional Brane-World Black Holes II: the general case

TL;DR

This paper investigates scalar field theories to find analytical 5D localized black hole solutions on branes, extending previous work by considering more general metrics and matter configurations, but encounters issues with bulk singularities.

Contribution

It introduces a generalized Vaidya metric ansatz and explores various scalar field theories to obtain localized black hole solutions in 5D brane-world models.

Findings

Solutions resemble Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom types.

The mass-function profile along the bulk does not eliminate singularities.

Certain matter configurations support localized black hole solutions.

Abstract

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.