BOUNDARY VALUE PROBLEMS FOR THE STATIONARY AXISYMMETRIC EINSTEIN EQUATIONS: A DISK ROTATING

Abstract. We solve a class of boundary value problems for the stationary ax-isymmetric 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