Schwarzschild black hole states and entropies on a nice slice

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.

37 pages, 19 figures, minor changes, references added, Updated to match the published version in EPJC

References in corpus (7)

• Islands in Schwarzschild black holes
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Notes on islands in asymptotically flat 2d dilaton black holes
• (Non)perturbative gravity, nonlocality, and nice slices
• Quantization in black hole backgrounds
• Density matrices in quantum gravity