TL;DR
This paper examines how different definitions of temperature in relativistic fluids, specifically in gravitational fields, relate to statistical mechanics, highlighting discrepancies between common relativistic temperature conventions.
Contribution
It compares Landau and Eckart temperature definitions in relativistic fluids and shows their inconsistency with the statistical-mechanical relation in gravitational fields.
Findings
Landau and Eckart temperatures differ in gravitational fields.
Neither temperature definition satisfies the relation 1/T=dS/dE.
Implications for relativistic fluid modeling in gravitational contexts.
Abstract
For static matter in a gravitational field, different conventions for equilibrium local temperature exist in the classic physics literature. We illustrate the difference between two popular conventions using black-body radiation in a spherically symmetric gravitational potential. Equilibrium temperatures defined by the "Landau frame" or "Eckart frame" prescriptions most commonly used in relativistic fluid dynamics do not satisfy the statistical-mechanical relation .
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Taxonomy
TopicsCosmology and Gravitation Theories · Pulsars and Gravitational Waves Research · High-pressure geophysics and materials