Black holes in which the electrostatic or scalar equation is solvable in closed form

Details Black holes in which the electrostatic or scalar equation is solvable in closed form Black holes in which the electrostatic or scalar equation is solvable in closed form

2005-07-18

arxiv.org/abs/gr-qc/0507072v1

Gen.Rel.Grav.37:2145-2163,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, no figure

Scientific paper

10.1007/s10714-005-0200-2

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerated horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordstrom black holes in higher dimensions.

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