Spacetime and universal soft modes: Black holes and beyond

Abstract

Recently, a coherent picture of the quantum mechanics of an evaporating black hole has been presented which reconciles unitarity with the predictions of the equivalence principle. The thermal nature of a black hole as viewed in a distance reference frame arises from entanglement between the hard and soft modes, generated by the chaotic dynamics at the string scale. In this paper, we elaborate on this picture, particularly emphasizing the importance of the chaotic nature of the string (UV) dynamics across all low energy species in generating large (IR) spacetime behind the horizon. Implications of this UV/IR relation include O(1) breaking of global symmetries at the string scale and a self-repair mechanism of black holes restoring the smoothness of their horizons. We also generalize the framework to other systems, including Rindler, de Sitter, and asymptotically flat spacetimes, and find a consistent picture in each case. Finally, we discuss the origin of the particular construction adopted in describing the black hole interior as well as the outside of a de Sitter horizon. We argue that the construction is selected by the quantum-to-classical transition, in particular the applicability of the Born rule in a quantum mechanical world.

Interior of a unitarily evaporating black hole

“…In this section and the next, we discuss a flat space (or a small AdS) black hole using the framework of Refs. [8,9]. A key feature of the framework is that the thermal nature of a black hole in a distant description can be viewed as arising from entanglement between hard and soft modes of lowenergy quantum fields.…”

“…For a black hole in asymptotically flat spacetime [or a small black hole in anti-de Sitter (AdS) spacetime], we work in the framework of Refs. [8,9]. This framework describes a black hole as a state in which the hard modes-the modes relevant for describing small objects around the black hole-are entangled in a generic manner with the soft modes-the degrees of freedom comprising the majority of the black hole.…”

“…can emerge through a coarse graining of the degrees of freedom that cannot be physically resolved by an infalling observer, whose consistency with black hole's unitary evolution is ensured by a specific entanglement structure between the hard modes, soft modes, and early radiation [9].…”

“…II, we describe the framework of Refs. [8,9], highlighting features relevant for our discussion. In Sec.…”

“…where ρ ϕ;n are reduced density matrices for the early radiation, whose n dependence is small and of order 1= ffiffiffiffiffiffiffiffiffiffiffiffiffi e S bh ðMÞ p . Note that in order to obtain the correct Boltzmann factor, ∝ e −E n =T H , it is essential that the coefficients c ni n a take generic values across all low-energy species, i.e., n runs over all low-energy species [9].…”