Three dimensional black holes and cylindrical general relativity

Abstract

A black string solution of the four dimensional Einstein-Hilbert action, S = 1 16πG ∫ d 4X −g (R−2Λ) , in a cylindrical spacetime is found. The three dimensional dilaton-gravity theory obtained through dimensional reduction, with action S = 1 2π ∫ d 3x −ge (R − 2Θ) , contains the corresponding three dimensional black hole solution. In this three dimensional theory one is able to define mass and angular momentum for the black hole using the Hamiltonian formulation. The causal structure is analyzed and the temperature of the black hole is computed.