Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String

Universe

卷:7

Herondy Francisco Santana Mota¹  Carlos Augusto Romero Filho¹  Valdir Barbosa Bezerra¹  Celio Rodrigues Muniz² 

[1] Departmento de Fisíca, Universidade Federal Paraíba, Caixa Postal 5008, João Pessoa 58059-900, PB, Brazil;

[2] Faculdade de Educação, Ciências e Letras de Iguatu, Universidade Estadual do Ceará, Iguatu 63502-253, CE, Brazil;

关键词: Casimir effect;    scalar field;    electromagnetic field;    massless spinor field;    Einstein universe;    Friedmann universe;   

DOI  :  10.3390/universe7070232

来源: DOAJ

【 摘 要 】

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic field in these backgrounds, multiplied by a parameter $\lambda =(1/\alpha )-1$, where $\alpha$ is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, $\mu$, by the expression $\alpha =1-G\mu$. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

【 授权许可】

Unknown