Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime
The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is dec...
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MDPI AG
2023-12-01
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| Online Access: | https://www.mdpi.com/2624-8174/5/4/74 |
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| author | Aram Saharian |
| author_facet | Aram Saharian |
| author_sort | Aram Saharian |
| collection | DOAJ |
| description | The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. |
| first_indexed | 2024-03-08T20:26:20Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2624-8174 |
| language | English |
| last_indexed | 2024-03-08T20:26:20Z |
| publishDate | 2023-12-01 |
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| series | Physics |
| spelling | doaj.art-b79091f32a974619affd4c43f8708e582023-12-22T14:33:14ZengMDPI AGPhysics2624-81742023-12-01541145116210.3390/physics5040074Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter SpacetimeAram Saharian0Institute of Physics, Yerevan State University, 1 Alex Manogian Street, Yerevan 0025, ArmeniaThe paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential.https://www.mdpi.com/2624-8174/5/4/74Casimir effectanti-de Sitter spacesurface energyRobin boundary conditions |
| spellingShingle | Aram Saharian Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime Physics Casimir effect anti-de Sitter space surface energy Robin boundary conditions |
| title | Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime |
| title_full | Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime |
| title_fullStr | Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime |
| title_full_unstemmed | Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime |
| title_short | Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime |
| title_sort | surface casimir densities on branes orthogonal to the boundary of anti de sitter spacetime |
| topic | Casimir effect anti-de Sitter space surface energy Robin boundary conditions |
| url | https://www.mdpi.com/2624-8174/5/4/74 |
| work_keys_str_mv | AT aramsaharian surfacecasimirdensitiesonbranesorthogonaltotheboundaryofantidesitterspacetime |