Black hole entropy and Lorentz-diffeomorphism Noether charge

Jacobson, Ted; Mohd, Arif

doi:10.1103/physrevd.92.124010

Cited by 107 publications

(205 citation statements)

References 19 publications

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“…This derivative has been introduced to avoid the divergence of the spin connection on the event horizon, even though the interior product between spin connection and Killing vector becomes finite on the bifurcation surface [63].…”

Section: Resultsmentioning

confidence: 99%

“…There were some studies of the properties of the linearized equation and holographic renormalization in MMG theory [61,62]. Nowadays there was a study about black hole entropy as the horizon Noether charge for diffeomorphism and local Lorentz symmetry [63]. It has also been performed some studies for the quasi-local conserved charges by considering the Lorentz diffeomorphism invariant gravity theories [64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

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

Nam

Park

2018

Eur. Phys. J. C

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nam

Park

2018

Eur. Phys. J. C

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“…In recent years, the connection between gravitation and thermodynamics has received much attention; see for example [1,2] and [8,[158][159][160][161], where the first and second laws of thermodynamics are thoroughly investigated. Through this section, first we obtain the unified first law of thermodynamics based on the (0, 0) component of the Einstein field equations introduced by Hayward; see [162,163] and [164].…”

Section: Thermodynamics Of An Einstein-cartan Cosmologymentioning

confidence: 99%

Emergent cosmos in Einstein–Cartan theory

et al. 2018

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Based on Padmanabhan's proposal, the accelerated expansion of the universe can be driven by the difference between the surface and bulk degrees of freedom in a region of space, described by the relation dV /dt = N sur − N bulk where N sur and N bulk = −N em + N de are the degrees of freedom assigned to the surface area and the matter-energy content inside the bulk such that the indices "em" and "de" represent energy-momentum and dark energy, respectively. In the present work, the dynamical effect of the Weyssenhoff perfect fluid with intrinsic spin and its corresponding spin degrees of freedom in the framework of Einstein-Cartan (EC) theory are investigated. Based on the modification of Friedmann equations due to the spin-spin interactions, a correction term for Padmanabhan's original relation dV /dt = N sur +N em −N de including the number of degrees of freedom related with these spin interactions is obtained through the modification in N bulk term as N bulk = −N em + N spin + N de leading to dV /dt = N sur + N em − N spin − N de in which N spin is the corresponding degrees of freedom related with the intrinsic spin of the matter content of the universe. Moreover, the validity of the unified first law and the generalized second law of thermodynamics for the Einstein-Cartan cosmos are investigated. Finally, by considering the covariant entropy conjecture and the bound resulting from the emergent scenario, a total entropy bound is obtained. Using this bound, it is shown that the for the universe as an expanding thermodynamical system, the total effective Komar energy never exceeds the square of the expansion rate with a factor of 3 4π .

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“…This is not an invariant quantity under the considered transformation. The Lorentz-Lie (L-L) derivative of the dreibein 1-form can be defined by [52] …”

Section: Quasi-local Conserved Chargesmentioning

confidence: 99%

“…By explicitly demanding that δ ξ e a = 0 when ξ is a Killing vector field, we find the following expression for χ ξ [50,52]:…”

Section: Quasi-local Conserved Chargesmentioning

confidence: 99%

Conserved charges of minimal massive gravity coupled to scalar field

Setare

Adami

2018

Eur. Phys. J. C

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Recently, the theory of topologically massive gravity non-minimally coupled to a scalar field has been proposed, which comes from the Lorentz-Chern-Simons theory (JHEP 06, 113, 2015), a torsion-free theory. We extend this theory by adding an extra term which makes the torsion to be non-zero. We show that the BTZ spacetime is a particular solution to this theory in the case where the scalar field is constant. The quasi-local conserved charge is defined by the concept of the generalized off-shell ADT current. Also a general formula is found for the entropy of the stationary black hole solution in context of the considered theory. The obtained formulas are applied to the BTZ black hole solution in order to obtain the energy, the angular momentum and the entropy of this solution. The central extension term, the central charges and the eigenvalues of the Virasoro algebra generators for the BTZ black hole solution are thus obtained. The energy and the angular momentum of the BTZ black hole using the eigenvalues of the Virasoro algebra generators are calculated. Also, using the Cardy formula, the entropy of the BTZ black hole is found. It is found that the results obtained in two different ways exactly match, just as expected.

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Black hole entropy and Lorentz-diffeomorphism Noether charge

Cited by 107 publications

References 19 publications

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

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

Emergent cosmos in Einstein–Cartan theory

Conserved charges of minimal massive gravity coupled to scalar field

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