Local toroidal black holes that are static and axisymmetric

Abstract

A solution, recently derived by Geroch and Hartle, representing local black holes with a toroidal topology, is constructed in a gauge in which the neighbourhood of the horizon is smoothly covered; and the metric tensor is written down explicitly in terms of Legendre polynomials. The construction is based on an approach suggested by Chandrasekhar for the construction of stationary axisymmetric solutions with horizons. The present method searches for a ‘background’ solution in a conceptually simple analytical way and seems applicable to the construction of stationary local black holes.