Thermodynamic equilibrium in general relativity

The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(...

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Detalles Bibliográficos
Autores: Lima, J. A. S., Del Popolo, A., Plastino, Ángel Ricardo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/175160
Acceso en línea:http://hdl.handle.net/11336/175160
Access Level:acceso abierto
Palabra clave:Thermodynamic Equilibrium
General Relativity
Tolman-Ehrenfest temperature
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
Descripción
Sumario:The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, Tg00(xi)=constant, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient g00(xi). By assuming the validity of Tolman-Ehrenfest "pocket temperature," Klein also proved a similar relation for the chemical potential, namely, μg00(xi)=constant. In this paper we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined.