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

Abstract

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.

arXiv comment20 pages, no figure

References in corpus (5)

• The self-force on a static scalar test-charge outside a Schwarzschild black hole
• Bekenstein Bound, Holography and Brane Cosmology in Charged Black Hole Backgrounds
• Black hole polarization and new entropy bounds
• Improved Upper Bound to the Entropy of a Charged System
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Cited by in corpus (8)

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• Self-energy of a scalar charge near higher-dimensional black holes
• Electrostatics in a simple wormhole revisited
• Electrostatic Potential of a Point Charge in a Brans-Dicke Reissner-Nordstrom Field
• Self-action in Gravity
• On the radiation field of a linearly accelerated charged particle in Born-Infeld theory
• Closed Form Solutions To Bosonic Perturbations In General Relativity