The Kerr metric is shown to be the exact nonlinear superposition of two Taub-NUT instantons of opposite chirality, explaining the Newman-Janis algorithm.
Macroscopic and Microscopic Description of Black Diholes
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abstract
We study configurations consisting of a pair of non-extremal black holes in four dimensions, both with the same mass, and with charges of the same magnitude but opposite sign---diholes, for short. We present such exact solutions for Einstein-Maxwell theory with arbitrary dilaton coupling, and also solutions to the U(1)^4 theories that arise from compactified string/M-theory. Despite the fact that the solutions are very complicated, physical properties of these black holes, such as their area, charge, and interaction energy, admit simple expressions. We also succeed in providing a microscopic description of the entropy of these black holes using the `effective string' model, and taking into account the interaction between the effective string and anti-string.
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Newman-Janis Algorithm from Taub-NUT Instantons
The Kerr metric is shown to be the exact nonlinear superposition of two Taub-NUT instantons of opposite chirality, explaining the Newman-Janis algorithm.