Abstract
By the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area/entropy spectra for the Schwarzschild-Tangherlini-type asymptotically flat or AdS vacuum black hole in arbitrary dimensions. Using the WKB approximation for black holes with large mass, we show that area/entropy is equally spaced for asymptotically flat black holes, while mass is equally spaced for asymptotically AdS black holes. Exact spectra can be obtained for toroidal AdS black holes in arbitrary dimensions including the three-dimensional BTZ black hole.
Highlights
Where gAB is an arbitrary two-dimensional Lorentzian metric on M2 and γab is the metric on the (n − 2)-dimensional maximally symmetric space Kn−2 with its curvature k
The ADM formalism of the Einstein equations shows that general relativity is a dynamically constrained system
Throat quantization pioneered by Louko and Mäkelä [1] is the reduced phase-space quantization for the spacetime (2) with a certain set of canonical variables
Summary
Where gAB is an arbitrary two-dimensional Lorentzian metric on M2 and γab is the metric on the (n − 2)-dimensional maximally symmetric space Kn−2 with its curvature k. This is the topological generalization of the Schwarzshild-Tangherlini solution in the presence of a cosmological constant. In order to investigate the quantum aspects of this Schwarzshild-Tangherlini-type black hole, one needs to quantize the Einstein equations (1). Reduced phase-space quantization is one possible way to quantize such a system, in which one performs canonical quantization on the constraint surface after solving all the (classical) constraint equations. It is hopeless to accomplish this with full generality. It is possible in the midisuperspace approach for the symmetric spacetime (2). Throat quantization pioneered by Louko and Mäkelä [1] is the reduced phase-space quantization for the spacetime (2) with a certain set of canonical variables
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