On the Entropy of a Quantum Field in the Rotating Black Holes

Abstract

By using the brick wall method we calculate the free energy and the entropy of the scalar field in the rotating black holes. As one approaches the stationary limit surface rather than the event horizon in comoving frame, those become divergent. Only when the field is comoving with the black hole (i.e. ${\Omega }_0={\Omega }_H$) those become divergent at the event horizon. In the Hartle-Hawking state the leading terms of the entropy are $A\frac{1}{h}+B\ln (h)+finite$, where $h$ is the cut-off in the radial coordnate near the horizon. In term of the proper distance cut-off $\epsilon$ it is written as $S=N{A}_H/{\epsilon }^2$. The origin of the divergence is that the density of state on the stationary surface and beyond it diverges.

Latex, 23 pages, 7 eps figures

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• Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field
• Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ Black Holes
• Entropies of Rotating Charged Black Holes from Conformal Field Theory at Killing Horizons
• Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields
• Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics
• Is the brick-wall model unstable for a rotating background?
• Statistical Mechanics on Axially-symmetric Space-times with the Killing Horizon and Entropy of Rotating Black Holes in Induced Gravity
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• Scalar Field Contribution to Rotating Black Hole Entropy
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• Gravity's Rainbow and Black Hole Entropy
• Entropy in the NUT-Kerr-Newman Black Holes Due to an Arbitrary Spin Field
• Rotating Black Hole Entropy from Two Different Viewpoints
• Can the "brick wall" model present the same results in different coordinate representations?
• Entropy of Kerr-Newman black hole to all orders in the Planck length
• Entropy of the Schwarzschild-de Sitter Black Hole due to arbitrary spin fields in different Coordinates
• Generalized Area Law under Multi-parameter Rotating Black Hole Spacetime