Can the "brick wall" model present the same results in different coordinate representations?
arXiv:gr-qc/0312078 · doi:10.1103/PhysRevD.69.024011
Abstract
By using the 't Hooft's "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropies arising from the quantum scalar field in different coordinate settings, such as the Painlevé and Lemaitre coordinates. At first glance, it seems that the entropies would be different from that in the standard Schwarzschild coordinate since the metrics in both the Painlevé and Lemaitre coordinates do not possess the singularity at the event horizon as that in the Schwarzschild-like coordinate. However, after an exact calculation we find that, up to the subleading correction, the statistical-mechanical entropies in these coordinates are equivalent to that in the Schwarzschild-like coordinate. The result is not only valid for black holes and de Sitter spaces, but also for the case that the quantum field exerts back reaction on the gravitational field provided that the back reaction does not alter the symmetry of the spacetime.
8 pages, Phys. Rev. D in press
References in corpus (33)
- Hawking radiation in different coordinate settings: Complex paths approach
- The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
- Black Hole Entropy without Brick Walls
- Method of complex paths and general covariance of Hawking radiation
- Rotating Dilaton Black Holes
- Thermal Fields, Entropy, and Black Holes
- Entropy for dilatonic black hole
- Conical geometry and quantum entropy of a charged Kerr black hole
- Black hole entropy without brick walls
- One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
- Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula
- On the Entropy of a Quantum Field in the Rotating Black Holes
- Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry. Quantum corrections to the black hole entropy
- Wavefunction of a Black Hole and the Dynamical Origin of Entropy
- Entropy in the Kerr-Newman Black Hole
- Effect of spins on the quantum entropy of black holes
- Black hole entropy: statistical mechanics agrees thermodynamics
- Renormalized black hole entropy in anti-de Sitter space via the "brick wall" method
- The Entropy of a Quantum Field in a Charged Kerr Black Hole
- Quantum entropy of the Kerr black hole arising from gravitational perturbation
- Entropy of 2+1 dimensional de Sitter space in terms of brick wall method
- Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field
- Divergences problem in black hole brick-wall model
- Non-minimal coupling and quantum entropy of black hole
- Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ Black Holes
- Thermodynamics of scalar fields in Kerr's geometry
- Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields
- Entropies of Rotating Charged Black Holes from Conformal Field Theory at Killing Horizons
- Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics
- Black Hole Entropy: Thermodynamics, Statistical-Mechanics and Subtraction Procedure
- Entropy of the Randall-Sundrum black brane world in the brick-wall method
- Brick Walls on the Brane
- Remarks on 't Hooft's Brick Wall Model