Tolman-like temperature gradients in stationary spacetimes
arXiv:1807.02915 · doi:10.1103/PhysRevD.98.064001
Abstract
It is (or should be) well known that specification of a heat bath requires both a temperature and a 4-velocity, the rest frame of the heat bath. In static spacetimes there is a very natural and unique candidate for the 4-velocity of the heat bath, the normalized timelike Killing vector. However in stationary non-static spacetimes the situation is considerably more subtle, and several different "natural" 4-velocity fields suitable for characterizing the rest frame of a heat bath can be defined - thus Buchdahl's 1949 analysis for the Tolman temperature gradient in a stationary spacetime is only part of the story. In particular, the heat bath most suitable for describing the Hawking radiation from a rotating black hole is best described in terms of a gradient flow normal to the spacelike hypersurfaces, not in terms of Killing vectors.
arXiv comment7 pages
References in corpus (16)
- Analogue Gravity
- Acoustic black holes: horizons, ergospheres, and Hawking radiation
- Gravity and the Thermodynamics of Horizons
- A new form of the Kerr solution
- The Kerr spacetime: A brief introduction
- The river model of black holes
- Acoustic geometry for general relativistic barotropic irrotational fluid flow
- Acoustic propagation in fluids: an unexpected example of Lorentzian geometry
- Tolman mass, generalized surface gravity, and entropy bounds
- Ideal Gas in a strong Gravitational field: Area dependence of Entropy
- Entropy bounds in terms of the w parameter
- Vorticity in analogue spacetimes
- Entropy of a box of gas in an external gravitational field revisited
- Entropy bounds for uncollapsed rotating bodies
- Gravity's universality: The physics underlying Tolman temperature gradients
- Entropy bounds for uncollapsed matter
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- Generating Kerr-anti-de Sitter thermodynamics
- Diffeomorphism symmetries near a timelike surface in black hole spacetime
- Evading the Trans-Planckian problem with Vaidya spacetimes
- Black hole thermodynamics probes the equivalence principle
- Thermodynamic parameters of fluids on conformally connected spacetimes