A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

Details A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

1995-03-27

arxiv.org/abs/gr-qc/9503052v1

Phys.Rev. D52 (1995) 4430-4439

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages (double-spaced) latex

Scientific paper

10.1103/PhysRevD.52.4430

The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as conjugate to a conical deficit angle, and (iv) the pair creation approach of Garfinkle, Giddings, and Strominger. All of these approaches have a more restrictive domain of applicability than the Noether charge approach. Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions. However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach. In the course of our analysis, we generalize the definition of Brown and York's quasilocal energy to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity. In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.

Affiliated with

Also associated with

No associations

Rating

A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-144143