Scalar Particles around a Rindler–Schwarzschild Wormhole
In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object m...
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| Format: | Article |
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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/2218-1997/8/12/616 |
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| author | C. R. Muniz H. R. Christiansen M. S. Cunha J. Furtado V. B. Bezerra |
| author_facet | C. R. Muniz H. R. Christiansen M. S. Cunha J. Furtado V. B. Bezerra |
| author_sort | C. R. Muniz |
| collection | DOAJ |
| description | In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell. |
| first_indexed | 2024-03-09T15:46:23Z |
| format | Article |
| id | doaj.art-0ebada86a61f4869b4fd3ca9616e377e |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T15:46:23Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-0ebada86a61f4869b4fd3ca9616e377e2023-11-24T18:28:55ZengMDPI AGUniverse2218-19972022-11-0181261610.3390/universe8120616Scalar Particles around a Rindler–Schwarzschild WormholeC. R. Muniz0H. R. Christiansen1M. S. Cunha2J. Furtado3V. B. Bezerra4Departamento de Física, FECLI, Universidade Estadual do Ceará, Av. Dário Rabelo, Iguatu 63500-518, BrazilDepartamento de Física, Instituto Federal de Ciências, Educação e Tecnologia, IFCE, Campus Maranguape, Maranguape 61940-750, BrazilDepartamento de Física, CCT, Universidade Estadual do Ceará, Fortaleza 60714-903, BrazilDepartamento de Física, CCT, Universidade Federal do Cariri, Juazeiro do Norte 63048-080, BrazilDepartamento de Física, CCEN, Universidade Federal da Paraíba, C.P. 5008, João Pessoa 58051-970, BrazilIn this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell.https://www.mdpi.com/2218-1997/8/12/616wormholesgeneral relativityscalar fieldsCasimir effectRindler space |
| spellingShingle | C. R. Muniz H. R. Christiansen M. S. Cunha J. Furtado V. B. Bezerra Scalar Particles around a Rindler–Schwarzschild Wormhole Universe wormholes general relativity scalar fields Casimir effect Rindler space |
| title | Scalar Particles around a Rindler–Schwarzschild Wormhole |
| title_full | Scalar Particles around a Rindler–Schwarzschild Wormhole |
| title_fullStr | Scalar Particles around a Rindler–Schwarzschild Wormhole |
| title_full_unstemmed | Scalar Particles around a Rindler–Schwarzschild Wormhole |
| title_short | Scalar Particles around a Rindler–Schwarzschild Wormhole |
| title_sort | scalar particles around a rindler schwarzschild wormhole |
| topic | wormholes general relativity scalar fields Casimir effect Rindler space |
| url | https://www.mdpi.com/2218-1997/8/12/616 |
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