Capacity of Entanglement and Replica Backreaction in RST Gravity

TL;DR

This paper analyzes the capacity of entanglement in the RST gravity model, revealing how replica backreaction influences entanglement properties and the Page transition in black hole physics.

Contribution

It provides the first analytical computation of the capacity of entanglement in the RST model, including the effects of replica backreaction and global constraints.

Findings

Generalized capacity is time independent for a single interval.

Interaction terms between replica fixed points affect capacity in two-interval cases.

Large two-QES capacity indicates non-uniform saddle competition near the Page transition.

Abstract

We compute the capacity of entanglement in two dimensional dilaton gravity in a setting where Hawking radiation, backreaction, and islands can be treated analytically. Our focus is the eternal black hole of the Russo Susskind Thorlacius model coupled to N conformal matter fields. Unlike previous gravitational computations, which were mostly carried out in JT gravity, the RST model forces one to deal with a genuinely dynamical conformal factor and with the global constraints of the replica construction. The main technical step is therefore to solve the replica deformation on the orbifold globally at first order near n=1, including the homogeneous sector fixed by single valuedness and by the requirement of a fixed microcanonical state. For a single interval we obtain a time independent generalized capacity, parallel to the generalized entropy. For two intervals, even in the late time factorization regime, the global solution generates an interaction term between replica fixed points; after Lorentzian continuation this produces a time dependent capacity on the two QES saddle, despite the corresponding entropy plateau. We discuss the regime of validity of the resulting expressions and explain how the large size of the two QES capacity implies a highly non uniform saddle competition near n=1, providing a concrete mechanism for sharp features of the capacity at the Page transition.