Reanalyzing an Evaporating Black Hole

TL;DR

<3-5 sentence high-level summary>Nomura presents a coherent, unitary framework for black holes formed by collapse and undergoing evaporation, where semiclassical physics describes only a small subset of degrees of freedom (the hard modes) while the vast soft-mode sector and early radiation act as a global purifier. The interior spacetime does not exist as a single global description; instead, it emerges through state-dependent coarse-graining into time-local effective theories that cover limited regions and collectively realize complementarity. The entanglement among hard modes, soft modes, and radiation is intrinsically tripartite (GHZ-like), ensuring no duplication of information within any single description and preventing horizon firewall behavior even as information returns to the environment according to the Page curve. The analysis extends to the Rindler limit and multi-black-hole configurations, showing that entangled BHs lack interior wormholes and that interior physics for each hole remains locally smooth, with information flow constrained by causal and holographic structure rather than global spacetime connectivity.

Abstract

A coherent picture of the quantum mechanics of a collapse-formed, evaporating black hole is presented. In a distant frame, semiclassical theory in the zone describes microscopic dynamics of only the "hard modes," the modes that are hard enough to be discriminated in the timescale of Hawking emission. The thermal nature of these modes arises from microcanonical typicality of the full black hole degrees of freedom, mostly composed of the "soft modes," the modes that cannot be discriminated at the semiclassical level. The hard modes are purified by a combined system of the soft modes and early Hawking radiation, but not by either of them separately. This intrinsically tripartite structure of entanglement is general, regardless of the age of the black hole. The interior spacetime emerges only at a coarse-grained level. To describe it, an effective theory can be erected at each time, which applies only to a limited spacetime region determined by the time at which the theory is erected. The entire interior of the black hole can be described only using multiple effective theories erected at different times, realizing the idea of complementarity. We analyze implications of the entanglement structure described here for various phenomena, including Hawking evaporation and general information retrieval. For multiple entangled black holes, it implies that semiclassical objects dropped into different black holes cannot meet in the interior, although each object smoothly enters the horizon of the black hole to which it is falling. We also discuss physics in Rindler space, elucidating how it is obtained as a smooth limit of the black hole physics.

Figures (4)

• Figure 1: The information transfer from an evaporating black hole occurs through negative energy-entropy excitations, created as a backreaction of Hawking emission occurring around the edge of the zone (left). This can be contrasted with the picture in which outgoing positive energy-entropy excitations carry information from the stretched horizon to the far region (right).
• Figure 2: The potential $\sqrt{V_l(r^*)}$ in units of $1/Ml_{\rm P}^2$, plotted as a function of $r_*/Ml_{\rm P}^2$. In the left panel, solid and dashed lines represent the potential for $\mu = 0$ and $1/Ml_{\rm P}^2$, respectively; for each value of $\mu$, $l = 0,1,2$ are plotted (from bottom to top). In the right panel, the cases of $\mu Ml_{\rm P}^2 = 0, 1, 2$ are plotted on a different scale (solid, dashed, and dotted, respectively), now for $l = 0,1,2,5$ for each value of $\mu$ (from bottom to top).
• Figure 3: Trajectories of an object released from $r = 4M l_{\rm P}^2$ at $(t - t_*)/Ml_{\rm P}^2 = -8, -10, -13, -20$, depicted in the non-null Kruskal-Szekeres coordinates $(u,v)$ (solid dark-blue lines, from right to left). The unfilled triangle-shaped region represents the positive $v$ part of the spacetime described by the effective theory of the interior built on the full microstate at $t = t_*$. The solid red line and dashed green lines represent the singularity, $v = \sqrt{u^2 + M^2 l_{\rm P}^2}$, and the horizon, $v = |u|$, respectively.
• Figure 4: A series of effective theories erected at different times (depicted by diamonds) covering the interior spacetime. The double red line and the dashed green line represent the singularity and the horizon, respectively. The figure is only a sketch; in particular, the second exterior and the white hole region in each effective theory do not belong to the original spacetime.