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Local temperature in general relativity

Hyeong-Chan Kim* and Youngone Lee†

  • School of Liberal Arts and Sciences, Korea National University of Transportation, Chungju 380-702, Korea

  • *hckim@ut.ac.kr
  • †youngone@ut.ac.kr

Phys. Rev. D 105, L081501 – Published 25 April, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L081501

Abstract

We examine the Tolman temperature by using Carter’s variational formalism of thermodynamics. We restrict our interests to fluids in thermal equilibrium that the heat does not propagate. We show that this condition presents a general formula for the local temperature gradient. We suggest a resolution of the recently addressed conflict in Tolman temperature when a chemical potential does not vanish.

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