Replica wormholes and capacity of entanglement

We consider the capacity of entanglement as a probe of the Hawking radiation in a two-dimensional dilaton gravity coupled with conformal matter of large degrees of freedom. A formula calculating the capacity is derived using the gravitational path integral, from which we speculate that the capacity has a discontinuity at the Page time in contrast to the continuous behavior of the generalized entropy. We apply the formula to a replica wormhole solution in an eternal AdS black hole coupled to a flat non-gravitating bath and show that the capacity of entanglement is saturated by the thermal capacity of the black hole in the high temperature limit.

Automated summary

The entanglement capacity is considered as a probe of Hawking radiation in a two-dimensional dilaton gravity system coupled with large degrees of freedom conformal matter. A formula for calculating the capacity is derived using the gravitational path integral, suggesting a discontinuity at the Page time. Application of the formula to a replica wormhole solution in an eternal AdS black hole coupled to a non-gravitating bath revealed saturation of the entanglement capacity by the thermal capacity of the black hole in the high temperature limit.