Black Holes in 2+1 Teleparallel Theories of Gravity

TL;DR

This paper explores black hole solutions within 2+1 dimensional teleparallel gravity, deriving a family of solutions, identifying the BTZ black hole as a special case, and confirming energy calculations via Hamiltonian and Brown-York methods.

Contribution

It presents the first application of Hamiltonian teleparallel gravity to 2+1 dimensions, deriving black hole solutions and establishing their energy equivalence with known methods.

Findings

Found a family of black hole solutions in 2+1 teleparallel gravity.

Identified the BTZ black hole as a unique solution fixing the theory's parameter.

Confirmed gravitational energy calculations match between Hamiltonian and Brown-York approaches.

Abstract

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.