Local free-fall temperature of a RN-AdS black hole
Yong-Wan Kim, Jaedong Choi, and Young-Jai Park
TL;DR
This paper defines a proper local temperature for freely falling observers outside a Reissner-Nordström-AdS black hole using GEMS geometry, extending to known black hole cases and ensuring finiteness at the horizon.
Contribution
It introduces a method to determine a finite local temperature for free-fall observers in RN-AdS black holes using GEMS embedding, encompassing various black hole solutions.
Findings
Proper local temperature remains finite at the event horizon.
The method extends to RN, Schwarzschild–AdS, and Schwarzschild black holes.
Provides a unified geometric approach to black hole thermodynamics.
Abstract
We use the global embedding Minkowski space (GEMS) geometries of a (3+1)-dimensional curved Reissner-Nordstr\"om(RN)-AdS black hole spacetime into a (5+2)-dimensional flat spacetime to define a proper local temperature, which remains finite at the event horizon, for freely falling observers outside a static black hole. Our extended results include the known limiting cases of the RN, Schwarzschild--AdS, and Schwarzschild black holes.
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