Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String
In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>...
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MDPI AG
2023-12-01
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| Online Access: | https://www.mdpi.com/2218-1997/10/1/20 |
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| author | Wagner Oliveira dos Santos Eugenio R. Bezerra de Mello |
| author_facet | Wagner Oliveira dos Santos Eugenio R. Bezerra de Mello |
| author_sort | Wagner Oliveira dos Santos |
| collection | DOAJ |
| description | In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>D</mi><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated. |
| first_indexed | 2024-03-08T10:33:29Z |
| format | Article |
| id | doaj.art-7a9cae71098a4d558faa7101705c0588 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-08T10:33:29Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-7a9cae71098a4d558faa7101705c05882024-01-26T18:42:59ZengMDPI AGUniverse2218-19972023-12-011012010.3390/universe10010020Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic StringWagner Oliveira dos Santos0Eugenio R. Bezerra de Mello1Departamento de Física, Universidade Federal da Paraíba, 58.059-970, Caixa Postal 5.008, João Pessoa 58059900, BrazilDepartamento de Física, Universidade Federal da Paraíba, 58.059-970, Caixa Postal 5.008, João Pessoa 58059900, BrazilIn this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>D</mi><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.https://www.mdpi.com/2218-1997/10/1/20cosmic stringmagnetic fluxde Sitter spacetimeflat boundaries |
| spellingShingle | Wagner Oliveira dos Santos Eugenio R. Bezerra de Mello Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String Universe cosmic string magnetic flux de Sitter spacetime flat boundaries |
| title | Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String |
| title_full | Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String |
| title_fullStr | Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String |
| title_full_unstemmed | Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String |
| title_short | Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String |
| title_sort | vacuum effects induced by a plate in de sitter spacetime in the presence of a cosmic string |
| topic | cosmic string magnetic flux de Sitter spacetime flat boundaries |
| url | https://www.mdpi.com/2218-1997/10/1/20 |
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