Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

TL;DR

This paper analyzes conserved quantities and entropy of BTZ black holes within a triad-affine BCEA theory, reformulating it as a metric theory (BCG) to clarify definitions and contributions of matter and gravity.

Contribution

It introduces a dual formulation of BCEA theory as a metric theory (BCG), resolving ambiguities in conserved quantities and clarifying matter and gravitational contributions.

Findings

Conserved quantities are consistently defined in both BCEA and BCG theories.

Entropy calculations align with earlier local formalism results.

The BCG formulation eliminates ambiguities in mass and angular momentum definitions.

Abstract

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.