Entropy of the BTZ Black Hole in 2+1 Dimensions
Sung-Won Kim, Won T. Kim, Young-Jai Park, and Hyeonjoon Shin
TL;DR
This paper calculates the entropy of a scalar field around a BTZ black hole, revealing the perimeter law and showing superradiant modes have minor contributions compared to non-superradiant modes.
Contribution
It provides a semi-classical derivation of the entropy and clarifies the roles of superradiant and non-superradiant modes in the entropy calculation.
Findings
Proper length from horizon to cutoff is independent of black hole parameters.
Superradiant modes contribute sub-leading order to entropy.
Non-superradiant modes dominate the entropy calculation.
Abstract
We semi-classically calculate the entropy of a scalar field in the background of the BTZ black hole, and derive the perimeter law of the entropy. The proper length from the horizon to the ultraviolet cutoff is independent of both the mass and the angular momentum of the black hole. It is shown that the superradiant scattering modes give the sub-leading order contribution to the entropy while the non-superradiant modes give the leading order one, and thus superradiant effect is minor.
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