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

Paul R. Anderson* and Amanda Peake

Shohreh Gholizadeh Siahmazgi†

  • *Contact author: anderson@wfu.edu
  • †Contact author: gholizs@wfu.edu
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Phys. Rev. D 113, 125030 – Published 25 June, 2026

DOI: https://doi.org/10.1103/dfcd-93tb

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 ⟨Tab⟩ for a massless minimally coupled scalar field in two dimensions. For Schwarzschild spacetime, the focus is on the Boulware and Unruh states. For the collapsing null shell spacetime, the in vacuum state is used. Instabilities of the Unruh 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.

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See Also

Quantum effects in 3+1 Schwarzschild–de Sitter spacetime: Properties of the Hadamard function

Ian M. Newsome, Silvia Pla, and Paul R. Anderson
Phys. Rev. D 111, L021702 (2025)

Article Text

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Outline

Information

Phys. Rev. D 113, 125030– Published 25 June, 2026
  • Received 31 October 2025
  • Accepted 13 April 2026
Article part of CHORUS
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