Black Holes in 2+1 Teleparallel Theories of Gravity

We apply the Hamiltonian formulation of teleparallel theories of gravity in 2+1 dimensions to a circularly symmetric geometry. We find a family of one-parameter black hole solutions. The BTZ solution fixes the unique free parameter of the theory. The resulting field equations coincide with the teleparallel equivalent of Einstein’s three-dimensional equations. We calculate the gravitational energy of the black holes by means of the simple expression that arises in the Hamiltonian formulation and conclude that the resulting value is identical to that calculated by means of the Brown-York method.