  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.
