Vacuum polarization and stress-energy of a quantum field inside of two-dimensional black holes

2025/10/18 by Paul Anderson, Anderson, Paul R., Amanda Peake +3
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.2510.16300

openalex publication_date 2025/10/18 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

Quantum effects are studied in both Schwarzschild spacetime and a spacetime in which a null shell collapses to form a black hole via the vacuum polarization ⟨ ϕ² ⟩ and stress-energy tensor ⟨ T_ab ⟩ for a massless minimally-coupled scalar field in two dimensions. For Schwarzschild spacetime, the Boulware, Unruh, and Hartle-Hawking states are considered. For the collapsing null shell spacetime, the in vacuum state is used. Instabilities of the Unruh, Hartle-Hawking, and in states resulting from the behavior of ⟨ ϕ² ⟩ in the regions inside and outside of the horizon are found. The question of how well the Unruh state for the eternal black hole approximates quantum effects in the interior of a black hole that forms from collapse is addressed.

Citations

• Computation of the semiclassical outflux emerging from a collapsing spherical null shell
• Notes on black-hole evaporation

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