Vacuum Fluctuations and the Renormalized Stress-Energy Tensor on a Cone with Arbitrary Boundary Conditions
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| Format: | Preprint |
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2025
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| _version_ | 1866908692759183360 |
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| author | Pitelli, João Paulo M. Mosna, Ricardo A. Ramos, Victor Hugo M. Barata, João C. A. |
| author_facet | Pitelli, João Paulo M. Mosna, Ricardo A. Ramos, Victor Hugo M. Barata, João C. A. |
| contents | We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass $M$ in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of boundary conditions was established by Kay and Studer in the early 1990s, but the consequences of their arbitrariness, represented here by a parameter $q$, for renormalized observables have not been examined. While for $M=0$ stability is achieved only under Dirichlet boundary conditions, for $M>q$ the field is stable and a localized mode emerges. This mode admits a natural interpretation as a covariant model of an extended particle detector, which allows us to investigate how such detectors modify the local vacuum structure. In this framework, the renormalized stress-energy tensor offers a natural way to quantify the influence of the detector on the surrounding spacetime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_20231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vacuum Fluctuations and the Renormalized Stress-Energy Tensor on a Cone with Arbitrary Boundary Conditions Pitelli, João Paulo M. Mosna, Ricardo A. Ramos, Victor Hugo M. Barata, João C. A. High Energy Physics - Theory General Relativity and Quantum Cosmology We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass $M$ in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of boundary conditions was established by Kay and Studer in the early 1990s, but the consequences of their arbitrariness, represented here by a parameter $q$, for renormalized observables have not been examined. While for $M=0$ stability is achieved only under Dirichlet boundary conditions, for $M>q$ the field is stable and a localized mode emerges. This mode admits a natural interpretation as a covariant model of an extended particle detector, which allows us to investigate how such detectors modify the local vacuum structure. In this framework, the renormalized stress-energy tensor offers a natural way to quantify the influence of the detector on the surrounding spacetime. |
| title | Vacuum Fluctuations and the Renormalized Stress-Energy Tensor on a Cone with Arbitrary Boundary Conditions |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.20231 |