Boundary value problems for the stationary axisymmetric Einstein equations: a disk rotating around a black hole

Abstract

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.

46 pages

References in corpus (2)

• General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
• Physically Realistic Solutions to the Ernst Equation on Hyperelliptic Riemann Surfaces

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