On the localisation of four-dimensional brane-world black holes. II: The general case. (English) Zbl 1331.83043
Summary: We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, 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 energy-momentum tensor which is non-isotropic in five dimensions, 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 for eliminating bulk singularities.
MSC:
| 83C57 | Black holes |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 81P15 | Quantum measurement theory, state operations, state preparations |
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