How can we erase states inside a black hole?

TL;DR

This paper explores the limitations of unitarity in black hole evaporation, showing that after the Page time, the internal state count increases, challenging the Bekenstein-Hawking entropy bound and supporting the remnant hypothesis.

Contribution

It demonstrates through toy models that unitary tracing-out processes are only possible before the Page time, impacting the understanding of black hole entropy and the information paradox.

Findings

Unitary tracing-out is only possible before the Page time.

Post-Page time, the internal states of black holes increase monotonically.

Black holes may violate the Bekenstein-Hawking entropy bound around the Page time.

Abstract

We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero energy system by maintaining unitarity. In this paper, based on some toy model calculations, we show that such a unitary tracing-out process is only possible before the Page time while it is impossible after the Page time. Hence, after the Page time, if we assume that the process is unitary and the Hawking pair forms a separable state, the internal number of states will monotonically increase, which is supported by the Almheiri-Marolf-Polchinski-Sully (AMPS) argument. In addition, the Hawking particles cannot generate randomness of the entire system; hence, the entanglement entropy cannot reach its maximum. Based on these results, we modify the correct form of the Page curve for the remnant picture. The most important conclusion is this: if we assume unitarity, semi-classical quantum field theory, and general relativity, then the black hole should violate the Bekenstein-Hawking entropy bound around the Page time at the latest; hence, the infinite production arguments for remnants might be applied for semi-classical black holes, which seems very problematic.