Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World
Abstract
In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize appropriate energy-momentum complexes. We investigate the energy-momentum distribution for a metric exterior to a spherically symmetric black hole in the brane world by applying the Landau-Lifshitz and Weinberg prescriptions. In both the aforesaid prescriptions, the energy thus obtained depends on the radial coordinate, the mass of the black hole and a parameter λ 0, while all the momenta are found to be zero. It is shown that for a special value of the parameter λ 0, the Schwarzschild space-time geometry is recovered. Some particular and limiting cases are also discussed.
- Publication:
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International Journal of Theoretical Physics
- Pub Date:
- March 2013
- DOI:
- 10.1007/s10773-012-1384-3
- arXiv:
- arXiv:1108.4397
- Bibcode:
- 2013IJTP...52..757R
- Keywords:
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- Energy-momentum complexes;
- Brane world black holes;
- General Relativity and Quantum Cosmology
- E-Print:
- 10 pages, sections 1 and 3 slightly modified, references modified and added