Locally Anisotropic (2+1)--Dimensional Black Holes

Abstract

In this paper we analyze the conditions when the Einstein equations with cosmological constant and matter describe (2+1)-dimensional generic locally anisotropic (la) spacetimes of generalized Finsler type. New classes of solutions for such la-spacetimes are constructed. There are investigated black la-holes with the induced from general relativity la-curvature and la-torsion and, as a particular case, the black la-hole solutions are found for teleparallel la-spaces. In a more general context we consider the la-renormalization of black hole constants via the receptivity of la-spacetimes. We speculate on the properties of (2+1)-dimensional black la-holes with unusual characteristics defined by la-interactions of matter and gravity. The thermodynamics of black la-holes is discussed in connection with a possible statistical mechanics background based on locally anisotropic variants of Chern-Simons theories.