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arXiv · 2510.16300

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

Paul R. Anderson·Amanda Peake·Shohreh Gholizadeh Siahmazgi
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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 $\langle \phi^2 \rangle$ and stress-energy tensor $\langle T_{ab} \rangle$ 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 \textit{in} vacuum state is used. Instabilities of the Unruh, Hartle-Hawking, and \textit{in} states resulting from the behavior of $\langle \phi^2 \rangle$ 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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Paul R. Anderson, Amanda Peake, Shohreh Gholizadeh Siahmazgi. 2025-10-18. Vacuum polarization and stress-energy of a quantum field inside of two-dimensional black holes. https://arxiv.org/abs/2510.16300

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