The Page curve of Hawking radiation from semiclassical geometry

TL;DR

This paper demonstrates that the entropy of Hawking radiation follows the Page curve by using higher-dimensional holographic duals and quantum extremal surfaces, connecting black hole interiors to radiation via entanglement wedges.

Contribution

It introduces a new rule for computing entanglement entropy involving 'islands' and relates quantum extremal surfaces to higher-dimensional RT/HRT surfaces in holography.

Findings

Entropy of Hawking radiation follows the Page curve.

Black hole interior becomes part of the radiation's entanglement wedge.

Proposes a new method for entropy calculation using islands.

Abstract

We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for "islands" in determining the entanglement wedge.