Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

TL;DR

This paper introduces a covariant regularization for entanglement entropy in curved spacetimes, analyzes entanglement dynamics during gravitational collapse and black hole evaporation, and explores models with different horizon structures to understand entropy behavior.

Contribution

It proposes a covariant regularization method for entanglement entropy and applies it to various black hole models, revealing new insights into entropy evolution and the role of horizons.

Findings

Radiation entropy diverges at evaporation end with an event horizon.

In nonsingular models, the generalized second law holds early but is violated later.

Radiation entropy can become negative before returning to zero.

Abstract

We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that $(i)$ in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, $(ii)$ in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, $(iii)$ at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.