For conformally related Einstein spacetimes, equilibrium fluid temperature and chemical potential both scale as the inverse conformal factor, preserving the ratio μ/T.
Hawking-Hayward quasi-local energy under conformal transformations
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We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a special case.
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Thermodynamic parameters of fluids on conformally connected spacetimes
For conformally related Einstein spacetimes, equilibrium fluid temperature and chemical potential both scale as the inverse conformal factor, preserving the ratio μ/T.