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

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 Ad S/C FT 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.

Generalized off-shell ADT conserved charges in the presence of matter Chern–Simons term

“…For OTT black hole, by using the off-shell ADT method in the first order gravity formalism, the conserved charges have been examined in review article [38] (see equations ( 499) and (518) therein), in which the mass and entropy are consistent with the first law of black hole thermodynamics but they are both twice the ones obtained from GR when the OTT black hole reduced to the BTZ one. The same results are obtained in [57] by using the Wald formalism in the first order gravity formalism, and confirmed in [58]. Actually, in this paper we proved the equivalence of the off-shell ADT method with the SPSM and the BBC formalisms, in which many conserved charges, such as the conserved charges in three-dimensional Lifshitz black hole and in warped AdS 3 black hole in NMG [18], have been checked to have the correct values consistent with the first law of black hole thermodynamics.…”

“…Although the off-shell ADT formalism already has many successful applications, there are still quite a few problems on the conserved charges to be studied. For example, the conserved charges for OTT black hole solution are obtained by off-shell ADT method and CPSM in [38] and in [57], respectively. Though the results coincide and consistent with the first law of black hole thermodynamics, the values of the conserved charges are twice of the ones obtained from GR when the OTT black hole reduces to the static and neutral BTZ black hole.…”

A note on the pp-wave solution of minimal massive 3D gravity coupled with Maxwell–Chern–Simons theory

“…Note that variation of metric function f (u, ρ) (and variation of β(u, ρ)) should be performed by considering the variation of wave profile functions C i that appear in the solution since these parameters behave as physical quantities. Then, it can be seen that the variation of co-frame and connection can be interpreted as difference between the solution and the background as is also indicated in [30]. On the other hand, the Maxwell field variations that we need can be presented as…”

“…We notice that to calculate the conserved charges associated with vector field ξ, the variation forms should be integrated at spatial infinity. Now, to obtain conserved charge for pp-wave solution, we closely follow the approach in [18,30] where in these works the conserved charges are obtained by calculating the charge variation forms for warped AdS solution. For the ppwave metric, note that ξ = ∂ ∂v := ξ v is the Killing vector that is obviously null.…”

Conserved charge of a gravity theory with p -form gauge fields and its property under Kaluza-Klein reduction

“…These modifications make it more operable to evaluate the Noether potential in terms of the corresponding current and the procedure of computation become more convenient to manipulate. Owing to these, the off-shell generalized formalism for the quasi-local conserved charges provides another fruitful way to evaluate the ADT charges for various theories of gravity and it has been extended to investigate the conserved charges of a wide scope of gravity theories with or without matter fields [10,11,12,13,14,15,16,17,18,19,20,21]. Particularly, in [10], the method in [9] was generalized to the gravity theories in the presence of matter fields.…”