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arXiv · 2303.03410

Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation

Chih-Hung Wu·Jiuci Xu
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Abstract

We start from $(3 + 1)$-dimensional Einstein gravity with minimally coupled massless scalar matter, through spherical dimensional reduction, the matter theory is non-minimally coupled with the dilaton in $(1 + 1)$-dimensions. Despite its simplicity, constructing a self-consistent one-loop effective theory for this model remains a challenge, partially due to a Weyl-invariant ambiguity in the effective action. With a universal splitting property for the one-loop action, the ambiguity can be identified with the state-dependent part of the covariant quantum stress tensor. By introducing on-shell equivalent auxiliary fields to construct minimal candidates of Weyl-invariant terms, we derive a one-parameter family of one-loop actions with unique, regular, and physical stress tensors corresponding to the Boulware, Hartle-Hawking and Unruh states. We further study the back-reacted geometry and the corresponding quantum extremal islands that were inaccessible without a consistent one-loop theory. Along the way, we elaborate on the implications of our construction for the non-minimal dilaton gravity model.

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Chih-Hung Wu, Jiuci Xu. 2023-03-06. Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation. https://doi.org/10.1007/jhep10(2023)094

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