Vacuum polarization in the Schwarzschild black hole with a global monopole

2026/02/11 by Leonardo G. Barbosa, Victor Hugo M. Ramos, Victor H. M. Ramos +1
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Charged black hole #Magnetic monopole #Polarization (electrochemistry) #Pulsars and Gravitational Waves Research #Schwarzschild radius #Vacuum polarization

paper · pdf · doi:10.1103/6l3r-yydt

openalex publication_date 2026/06/23 · openalex created_date 2026/06/24 · openalex updated_date 2026/08/01

Abstract

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 ⟨ Ψ² ⟩_\textrmren. 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(η²), we find that ⟨ Ψ² ⟩_\textrmren 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. We also investigate whether an analogous decomposition holds for ⟨ T^μ_\phantomμμ⟩_\textrmren when it is determined by this method. Our result parallels earlier analyses of Schwarzschild black holes pierced by a cosmic string.

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