Kerr and Schwarzschild black-holes in three-dimensional relativity

We consider the Kerr and Schwarzschild black-hole space-times in the framew ork of a three-dimensional formulation of relativistic kinematics and field dynamics, in which local physical observers are represented by non-singula r vector fields of bounded length in a three-dimensional pseudo-Riemannian space. A space-time is represented by a pair of 3-metric and a fundamental 3-vector field satisfying a set of basic equations, each solution of which determines uniquely a solution of the vacuum Einstein field equations. It i s shown that the only spherically symmetric solution of our basic equations leads to the Schwarzschild space-time, thereby proving a version of Birkof f's theorem in this formalism. The Schwarzschild horizon and the Kerr stati onary limit are both related to the upper bound of the length of the corres ponding physical 3-vector fields. An example of a solution of the vacuum Ei nstein field equations shows that nonstationary space-times can also be for mulated in this three-dimensional relativity. (C) 2000 American Institute o f Physics. [S0022-2488(00)00911-7].