Effect of Non-Extensive Parameter on Page Curve

TL;DR

This paper investigates how non-extensive entropy corrections affect the Page curve of black holes, showing that the entanglement entropy saturates to a non-extensive Bekenstein-Hawking entropy and analyzing the impact on the Page time.

Contribution

It introduces a non-extensive entropy correction into the quantum extremal surface framework to study black hole information dynamics and the Page curve.

Findings

Entanglement entropy saturates to a non-extensive Bekenstein-Hawking entropy.

The Page time depends on the non-extensive parameters.

The information paradox persists with non-extensive entropy corrections.

Abstract

This work employs the quantum extremal surface framework to compute the Page curve for black holes corrected by non-extensive entropy. The entropy of Hawking radiation increases linearly with time, leading to the persistence of the information paradox for non-extensive entropy-corrected black holes. At late time, we extremize the generalized entropy functional; incorporating contributions from both matter and the quantum extremal island, we establish that the entanglement entropy of Hawking radiation saturates to the non-extensive extension of the Bekenstein-Hawking entropy. Finally, we study the dependence of non-extensive parameters on the Page time.