Hawking Temperature and the Inverse-Radius Scale of the Horizon
Michael R.R. Good, Yen Chin Ong
TL;DR
This paper explores the heuristic relationship between black hole horizon radius and Hawking temperature, revealing its limitations for complex black holes and uncovering connections with black hole thermodynamics.
Contribution
It clarifies why the inverse-radius heuristic fails for Kerr and Reissner-Nordström black holes and links this failure to black hole thermodynamic properties.
Findings
The inverse-radius heuristic works for Schwarzschild black holes.
It fails for Kerr and Reissner-Nordström black holes.
Connections with black hole thermodynamics are uncovered.
Abstract
The Hawking temperature of a Schwarzschild black hole can be heuristically derived by identifying the temperature with the inverse radius of the horizon up to a multiplicative constant. This does not work for more general black holes such as the Kerr and Reissner-Nordstr\"om solutions. Expounding on the details of how it fails to work nevertheless uncovers interesting connections with the "spring constant" of black holes and with black hole thermodynamics.
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Taxonomy
TopicsSpaceflight effects on biology · Aerospace Engineering and Energy Systems · Wind and Air Flow Studies