The Interior of a Unitarily Evaporating Black Hole

TL;DR

Nomura analyzes how to realize the interior of a unitarily evaporating black hole in a microscopic theory. He shows that interior operators can be defined globally as linear operators across the full microstate space, with the interior algebra holding up to corrections that are exponentially suppressed by the ratio of excitation energy to the Hawking temperature $E_{\text{exc}}/T_{\rm H}$. A key distinction is drawn between young and old black holes: young holes admit interior operators acting within the black hole’s hard/soft sector, while old holes require involvement of early radiation; this is elucidated for both flat-space and large AdS black holes and is tied to Page-time physics. The work connects to entanglement wedge reconstruction, arguing that semiclassical spacetime emergence hinges on the existence of approximately global interior operators, and proposes a decomposition ${\cal H}_{\rm exc}\otimes{\cal H}_{\rm vac}$ to capture the emergent interior dynamics.

Abstract

We study microscopic operators describing the experience of an observer falling into the horizon of a unitarily evaporating black hole. For a young black hole, these operators can be taken to act only on the degrees of freedom in the black hole region: the soft---or stretched horizon---modes as well as the semiclassical modes in the zone region. On the other hand, for an old black hole, the operators must also involve radiation emitted earlier; the difference between the two cases comes from statistics associated with the coarse-graining performed to obtain the effective theory of the interior. We find that the operators relevant for the interior theory can be defined globally as standard linear operators throughout the microstates, which obey the correct algebra up to corrections exponentially suppressed in the ratio of excitation energy to the Hawking temperature. We conjecture that the existence of such global operators is required for the emergence of the semiclassical picture. We also elucidate relation between the present construction and entanglement wedge reconstruction of the interior.

Figures (1)

• Figure 1: Radiation of a state given at time $t$ can represent the hard modes hitting the stretched horizon at or before $t_{\rm w}$ ($< t$) and the soft modes entangled with them, through time evolution. This allows us to construct the effective interior theory erected at $t_{\rm w}$ whose operators act only on radiation at $t$; these operators, however, cannot describe the future of the zone at $t_{\rm w}$, since the radiation cannot represent hard modes there nor the soft modes entangled with them. A similar construction works for effective theories erected at times earlier than $t_{\rm w}$, implying that we can reconstruct the spacetime region denoted by ${\cal E}_{\rm rad}$, which reproduces the entanglement wedge of the radiation at time $t$. This region, however, cannot describe the fate of a falling object located in the zone at time $t$ (segment $CA$), which occurs in the future of $C$ (shaded). To construct an effective theory describing (a part of) this region building on the state at time $t$, we need operators that act both on the soft modes and radiation (in addition to those acting on the hard modes).