Ehrenfest–Tolman effect

The Ehrenfest–Tolman effect (also known as the Tolman–Ehrenfest effect), created by Richard C. Tolman and Paul Ehrenfest, argues that temperature is not constant in space at thermal equilibrium, but varies with the spacetime curvature. Specifically, it depends on the spacetime metric. In a stationary spacetime with timelike Killing vector field ${\displaystyle \xi }$, the temperature ${\displaystyle T}$ satisfies instead the Tolman-Ehrenfest relation: ${\displaystyle T\,||\xi ||=\mathrm {constant} }$, where ${\displaystyle ||\xi ||={\sqrt {g_{ab}\xi ^{a}\xi ^{b}}}}$ is the norm of the timelike Killing vector field.

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