Relativeness in quantum gravity: limitations and frame dependence of semiclassical descriptions

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.1 Note that the concepts of the breakdown of a semiclassical description and that of semiclassical field theory are not the same-there can be phase space regions in which an object can be well described as a string (or brane) propagating in spacetime, but not as a particle.2 The stretched horizon is located at a microscopic distance outside of the mathematical horizon, and is regarded as a physical (timelike) membrane which may be physically excited [4].

Flat-space quantum gravity in theAdS/CFTcorrespondence

“…Below, we discuss what the picture of evaporating black holes proposed in Refs. [15,16] to avoid the information problem [1,3] implies for CFTs in the framework described in the previous section. Since CFTs are well-defined, this in principle allows us to test (aspects of) the proposal, perhaps with the future development of techniques to analyze CFTs.…”

“…In particular, we describe how the picture of an evaporating black hole in Refs. [15,16], proposed to solve the black hole information problem [1,3], is translated into the CFT language given here. This has at least two virtues.…”

“…In principle, this allows us to test (aspects of) the picture of Refs. [15,16], perhaps with some future theoretical developments. Second, the translated CFT description clarifies the concept of spacetime-matter duality introduced in Refs.…”

“…Second, the translated CFT description clarifies the concept of spacetime-matter duality introduced in Refs. [15,16]: the black hole microstates play roles of both spacetime and matter, but in fact are neither. In the CFT language, this can be stated as properties exhibited by the operators corresponding to black hole microstates.…”

“…We finally apply the scheme to black hole states to see how the picture of Refs. [15,16] may be realized in CFTs. Section 4 is devoted to the summary and discussion.…”