Stationary Axisymmetric Black Holes, $N=2$ Superstring, and Self-Dual Gauge or Gravity Fields

Abstract

We present interesting relationship between what are called stationary axisymmetric black hole solutions for the vacuum Einstein equations in the ordinary four-dimensions and exact solutions for self-dual Yang-Mills fields in flat $2+2$ dimensions which are nothing but the consistent backgrounds for $N=2$~ open superstring. We show that any stationary axisymmetric black hole solution for the former automatically provides an exact solution for the latter. We also give a nice relation between the physical parameters of black holes and an invariant integral analogous to instanton charges for such a self-dual Yang-Mills solution. This result indicates that any general black hole solution in the usual four-dimensions can be the background of $N=2$~ superstring at the same time. We also give an interesting embedding of stationary axisymmetric solutions into the background of $N=2$~ closed superstring. Finally we show some indication that the Kerr solution with naked singularity (for $a>m$) is nothing else than the gravitational field generated by a closed string.

15 pages

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• Lightlike limit of the boosted Kerr black holes in higher-dimensional spacetimes
• Axisymmetric Gravitational Solutions as Possible Classical Backgrounds around Closed String Mass Distributions
• Gravitational fields as generalized string models
• Phase transition of spacetime: particles as black holes in anti-de Sitter space