Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary
In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/11/597 |
| _version_ | 1797463844043358208 |
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| author | Herondy F. S. Mota Celio R. Muniz Valdir B. Bezerra |
| author_facet | Herondy F. S. Mota Celio R. Muniz Valdir B. Bezerra |
| author_sort | Herondy F. S. Mota |
| collection | DOAJ |
| description | In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics. |
| first_indexed | 2024-03-09T17:57:29Z |
| format | Article |
| id | doaj.art-c43a5f323a934c609c443231176a0215 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T17:57:29Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-c43a5f323a934c609c443231176a02152023-11-24T10:16:07ZengMDPI AGUniverse2218-19972022-11-0181159710.3390/universe8110597Thermal Casimir Effect in the Einstein Universe with a Spherical BoundaryHerondy F. S. Mota0Celio R. Muniz1Valdir B. Bezerra2Departamento de Física, Universidade Federal da Paraíba, Caixa Postal, João Pessoa 58050-585, PB, BrazilFaculdade de Educação, Ciências e Letras de Iguatu, Universidade Estadual do Ceará, Av. Dário Rabelo, Iguatu 63500-000, CE, BrazilDepartamento de Física, Universidade Federal da Paraíba, Caixa Postal, João Pessoa 58050-585, PB, BrazilIn the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics.https://www.mdpi.com/2218-1997/8/11/597Einstein universespherical boundarythermal correctionCasimir energy |
| spellingShingle | Herondy F. S. Mota Celio R. Muniz Valdir B. Bezerra Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary Universe Einstein universe spherical boundary thermal correction Casimir energy |
| title | Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary |
| title_full | Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary |
| title_fullStr | Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary |
| title_full_unstemmed | Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary |
| title_short | Thermal Casimir Effect in the Einstein Universe with a Spherical Boundary |
| title_sort | thermal casimir effect in the einstein universe with a spherical boundary |
| topic | Einstein universe spherical boundary thermal correction Casimir energy |
| url | https://www.mdpi.com/2218-1997/8/11/597 |
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