Microcanonical Action and the Entropy of Hawking Radiation

Understand

The island formula -- an extremization prescription for generalized entropy -- is known to result in a unitary Page curve for the entropy of Hawking radiation.

• This semi-classical entropy formula has been derived for Jackiw-Teitelboim (JT) gravity coupled to conformal matter using the "replica trick" to evaluate the Euclidean path integral.
• Alternatively, for eternal Anti-de Sitter black holes, we derive the extremization of generalized entropy from minimizing the microcanonical action of an entanglement wedge.
• The on-shell action is minus the entropy and arises in the saddle-point approximation of the (nonreplicated) microcanonical path integral.