Schwarzschild black hole states and entropies on a nice slice

TL;DR

This paper constructs a quantum gravity state on a nice slice of a Schwarzschild black hole, analyzing its topology, geometry, and thermodynamic entropy, and discusses entanglement entropy and connections to replica wormholes.

Contribution

It introduces a new quantum state on a nice slice that avoids strong curvature regions and computes its semiclassical entropy, linking it to Hawking's results and entanglement entropy.

Findings

The entropy on a nice slice matches Hawking's semiclassical entropy.

The state is not globally pure but yields consistent thermodynamic results.

Discussion of entanglement entropy and relation to replica wormhole calculations.

Abstract

In this work, we define a quantum gravity state on a nice slice. The nice slices provide a foliation of spacetime and avoid regions of strong curvature. We explore the topology and the geometry of the manifold obtained from a nice slice after evolving it in complex time. We compute its associated semiclassical thermodynamics entropy for a 4d Schwarzschild black hole. Despite the state one can define on a nice slice is not a global pure state, remarkably, we get a similar result to Hawking's calculation. In the end, we discuss the entanglement entropy of two segments on a nice slice and comment on the relation of this work with the replica wormhole calculation.