A toy model that puts blackbody oscillators on a circle yields curvature-dependent Planck, Stefan-Boltzmann, Rayleigh-Jeans, and Wien laws, with larger curvature producing a redshifted and reduced spectrum.
Demons in Black Hole Thermodynamics: Bekenstein and Hawking
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abstract
This paper comprehensively explores Stephen Hawking's interaction with Jacob Bekenstein. Both Hawking and Bekenstein benefited from the interaction with each other. It is shown that Hawking's interaction with Bekenstein drove him to solve the problems in Bekenstein's black hole thermodynamics in terms of a new thermal radiation mechanism. Hawking derived the thermal radiation using a semiclassical approximation in which the matter fields are treated quantum mechanically on a classical spacetime background. Hawking's semiclassical approximation yielded a simple formula for the entropy of the black hole, which turned out to be equivalent to Bekenstein's equation for entropy.
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Effects of Spatial Curvature on Blackbody Radiation: Modifications to Energy Distribution and Fundamental Laws
A toy model that puts blackbody oscillators on a circle yields curvature-dependent Planck, Stefan-Boltzmann, Rayleigh-Jeans, and Wien laws, with larger curvature producing a redshifted and reduced spectrum.