Mass and angular momentum of black holes in 3D gravity theories with first order formalism

TL;DR

This paper applies the Wald formalism in the first order approach to compute masses, angular momenta, and entropy of black holes in various 3D gravity theories, enhancing understanding of conserved charges and thermodynamics.

Contribution

It extends the Wald formalism to first order formalism in 3D gravity, providing explicit calculations for black hole charges in multiple theories including topologically and new massive gravity.

Findings

Calculated masses and angular momenta for black holes in various 3D gravity theories.

Derived entropy and central charges for new type black holes.

Suggested temperature relations in the context of AdS/CFT correspondence.

Abstract

We apply the Wald formalism to obtain masses and angular momenta of black holes in three dimensional gravity theories using the first order formalism. Wald formalism suggests that the entropy of a black hole can be defined by an integration of a conserved charge on the bifurcation horizon, and mass and angular momentum of a black hole as an integration of some charge variation form at spatial infinity. The action of three dimensional gravity theories can be represented by a form including some auxiliary fields. As well-known examples we have calculated masses and angular momenta of some black holes in topologically massive gravity and new massive gravity theories using the first order formalism. We have also calculated mass and angular momentum of BTZ black hole and new type black hole in minimal massive gravity theory with the action represented by the first order formalism. We have also calculated the entropy and central charges of new type black hole. According to $AdS/CFT$ correspondence we suggest that the left and right moving temperatures should be equal to the Hawking temperature in the case of new type black hole in minimal massive gravity.