Vacuum polarization in the Schwarzschild black hole with a global monopole
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| Format: | Preprint |
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2026
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| _version_ | 1866917268065091584 |
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| author | Barbosa, Leonardo G. Ramos, Victor H. M. Pitelli, João Paulo M. |
| author_facet | Barbosa, Leonardo G. Ramos, Victor H. M. Pitelli, João Paulo M. |
| contents | We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $Ψ$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle Ψ^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $η$ and retaining terms through $O(η^2)$, we find that $\langle Ψ^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result - with the event horizon radius modified by the presence of $η$. Our result parallels earlier analyses for Schwarzschild black holes pierced by a cosmic string. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_10899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vacuum polarization in the Schwarzschild black hole with a global monopole Barbosa, Leonardo G. Ramos, Victor H. M. Pitelli, João Paulo M. General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $Ψ$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle Ψ^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $η$ and retaining terms through $O(η^2)$, we find that $\langle Ψ^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result - with the event horizon radius modified by the presence of $η$. Our result parallels earlier analyses for Schwarzschild black holes pierced by a cosmic string. |
| title | Vacuum polarization in the Schwarzschild black hole with a global monopole |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.10899 |