A coarse simplicial quantum gravity model produces semiclassical saddles whose swap entropy rises and then falls, reproducing the Page transition at n→1+.
The imaginary part of the gravitational action at asymptotic boundaries and horizons
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abstract
We study the imaginary part of the Lorentzian gravitational action for bounded regions, as described in arXiv:1301.7041. By comparing to a Euclidean calculation, we explain the agreement between the formula for this imaginary part and the formula for black hole entropy. We also clarify the topological structure of the imaginary part in Lovelock gravity. We then evaluate the action's imaginary part for some special regions. These include cylindrical slabs spanning the exterior of a stationary black hole spacetime, 'maximal diamonds' in various symmetric spacetimes, as well as local near-horizon regions. In the first setup, the black hole's entropy and conserved charges contribute to the action's imaginary and real parts, respectively. In the other two setups, the imaginary part coincides with the relevant entropy.
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Studying replica wormholes and the Page curve with simplicial quantum gravity
A coarse simplicial quantum gravity model produces semiclassical saddles whose swap entropy rises and then falls, reproducing the Page transition at n→1+.