TELEPARALLEL THEORY OF (2+1)-DIMENSIONAL GRAVITY

A theory of (2+1)-dimensional gravity is developed on the basis of the Weitzenbock space-time characterized by the metricity condition and by the vanishing curvature tenser. The fundamental gravitational field variables are dreibein fields and the gravity is attributed to the torsion. The most general gravitational Lagrangian density quadratic in the torsion tenser is given by L(G)=alpha t(klm)t(klm)+beta v(k)v(k)+gamma a(klm). Here, t(klm), v(k), and a(klm) are irreducible components of the torsion tensor, and a, P, and gamma are real parameters. A condition is imposed on alpha and beta by the requirement that the theory has a correct Newtonian limit. A static circularly symmetric exact solution of the gravitational field equation in the vacuum is given. It gives space-times quite different from each other, according to the signature of ap. These space-times have event horizons, if and only if cr(3 alpha+4 beta)<0. Singularity structures of these space-times are also examined.