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(...
| Autores: | , , |
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| 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 |
| 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. |
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