Page curves for tripartite systems

TL;DR

This paper models information flow in tripartite systems resembling black hole evaporation, analyzing how information is distributed among radiation, remnants, and their mutual correlations, revealing conditions affecting information retention and the black hole information paradox.

Contribution

It introduces a tripartite system framework to study information distribution during black hole evaporation, highlighting the role of remnant size in information retention and complementarity.

Findings

If the remnant has fewer states than radiation, information is stored in radiation and mutual information.

If the remnant has more states, information resides mainly in the remnant and mutual information.

Hawking radiation contains information only if the remnant's states are not too large.

Abstract

We investigate information flow and Page curves for tripartite systems. We prepare a tripartite system (say, A, B, and C) of a given number of states and calculate information and entropy contents by assuming random states. Initially, every particle was in A (this means a black hole), and as time goes on, particles move to either B (means Hawking radiation) or C (means a broadly defined remnant, including a non-local transport of information, the last burst, an interior large volume, or a bubble universe, etc.). If the final number of states of the remnant is smaller than that of Hawking radiation, then information will be stored by both of the radiation and the mutual information between the radiation and the remnant, while the remnant itself does not contain information. On the other hand, if the final number of states of the remnant is greater than that of Hawking radiation, then the radiation contains negligible information, while the remnant and the mutual information between the radiation and the remnant contain information. Unless the number of states of the remnant is large enough compared to the entropy of the black hole, Hawking radiation must contain information; and we meet the menace of black hole complementarity again. Therefore, this contrasts the tension between various assumptions and candidates of the resolution of the information loss problem.