Relativeness in Quantum Gravity: Limitations and Frame Dependence of Semiclassical Descriptions

TL;DR

The paper addresses how to reconcile unitarity with semiclassical gravity in black hole evolution by identifying the Bekenstein-Hawking entropy as the count of microstates that must be coarse grained to obtain semiclassical spacetime. It introduces extreme relativeness and spacetime matter duality, showing that vacuum degrees of freedom are distributed frame-dependently and that interior spacetime can emerge in infalling frames while remaining consistent with distant frame descriptions through complementarity. By detailing microscopic unitary processes for Hawking emission and mining, and contrasting them with semiclassical thermality, the work provides a concrete mechanism for information preservation and a prescription for how general coordinate transformations may operate in full quantum gravity beyond semiclassical limits. The overall result is a coherent, unitary account of black hole formation, evaporation, and interior emergence that avoids firewalls and clarifies the role of frame dependence in quantum gravity.

Abstract

Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality---a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.

Figures (4)

• Figure 1: A schematic picture of the elementary Hawking emission process; time flows from the top to the bottom. The edge of the zone, i.e. the barrier region of the effective gravitational potential, is shown by a portion of a dashed circle at each moment in time. The emitted Hawking quanta as well as negative energy excitations are depicted by arrows (solid and dotted, respectively) although they are mostly $s$-waves.
• Figure 2: Time reversal of the Hawking emission process (a) as opposed to the process in which generic incoming radiation enters into the zone of a usual black hole (b). The former is an entropy decreasing process requiring an exponentially fine-tuned initial state, while the latter is a standard process respecting the (generalized) second law of thermodynamics.
• Figure 3: A schematic depiction of the fate of an elementary particle of mass $m$ ($1/M l_{\rm P}^2 \ll m \ll 1/l_*$) dropped into a black hole, viewed in a distant reference frame. As the particle falls, its local energy blueshifts and exceeds the string/cutoff scale $1/l_*$ before it hits the stretched horizon. After this point, stringy effects could become important, although the semiclassical description of the object may still be applicable. The object hits the stretched horizon at a Schwarzschild time of about $4 M l_{\rm P}^2 \ln(M l_{\rm P}^2/l_*)$ after the drop. After this time, the semiclassical description of the object is no longer applicable, and the information about the object will be encoded in the index $\bar{a}$, representing excitations of the stretched horizon. (This information will further move to the vacuum index $k$ later, so that it can be extracted by an observer in the asymptotic region via the Hawking emission or mining process.)
• Figure 4: A sketch of an infalling reference frame in an Eddington-Finkelstein diagram: the horizontal and vertical axes are $r$ and $t^* = t+r^*-r$, respectively, where $r^*$ is the tortoise coordinate. The thick (blue) line denotes the spacetime trajectory of the origin, $p_0$, of the reference frame, while the thin (red) lines represent past-directed light rays emitted from $p_0$. The shaded area is the causal patch associated with the reference frame, and the dotted (green) line represents the stretched "horizon" as viewed from this reference frame.