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Origin of the blackhole information paradox

Ram Brustein

TL;DR

The paper argues that the black-hole information paradox originates from imposing a strictly classical geometry with a horizon on quantum physics. By treating the geometry as quantum and allowing horizon fluctuations, the horizon is effectively destroyed except in the strict classical limit where $\lambda_{BH}/R_S \to 0$, and the paradox shifts from a breakdown of fundamental principles to a problem of describing strong gravity. It develops a framework based on horizon-entropy variables, e.g., the canonical pair $[\widehat{\Theta},\widehat{S}_W]=i\hbar$, and horizon-radius wavefunctions which together show that horizonless, off-shell geometries arise in the quantum theory. Consequently, unitarity is preserved in the global quantum state, and the information is not lost but rather is encoded in the strong-gravity region; the challenge becomes constructing a microscopic description of this region rather than debating information loss. This reframes the information paradox as a strong-gravity problem and motivates further quantum-gravity work to characterize collapse and high-curvature regimes.

Abstract

It is argued that the blackhole information paradox originates from treating the blackhole geometry as strictly classical. It is further argued that the theory of quantum fields in a classical curved space with a horizon is an ill posed problem. If the geometry is allowed to fluctuate quantum mechanically, then the horizon effectively disappears. The sharp horizon emerges only in the classical limit when the ratio of the Compton wavelength of the black hole to its Schwarzschild radius vanishes. The region of strong gravity that develops when matter collapses to form the blackhole remains visible to the whole of spacetime and has to be described by a microscopic theory of strong gravity. The arguments imply that the information paradox is demoted from a paradox involving fundamental principles of physics to the problem of describing how matter at the highest densities gravitates.

Origin of the blackhole information paradox

TL;DR

The paper argues that the black-hole information paradox originates from imposing a strictly classical geometry with a horizon on quantum physics. By treating the geometry as quantum and allowing horizon fluctuations, the horizon is effectively destroyed except in the strict classical limit where , and the paradox shifts from a breakdown of fundamental principles to a problem of describing strong gravity. It develops a framework based on horizon-entropy variables, e.g., the canonical pair , and horizon-radius wavefunctions which together show that horizonless, off-shell geometries arise in the quantum theory. Consequently, unitarity is preserved in the global quantum state, and the information is not lost but rather is encoded in the strong-gravity region; the challenge becomes constructing a microscopic description of this region rather than debating information loss. This reframes the information paradox as a strong-gravity problem and motivates further quantum-gravity work to characterize collapse and high-curvature regimes.

Abstract

It is argued that the blackhole information paradox originates from treating the blackhole geometry as strictly classical. It is further argued that the theory of quantum fields in a classical curved space with a horizon is an ill posed problem. If the geometry is allowed to fluctuate quantum mechanically, then the horizon effectively disappears. The sharp horizon emerges only in the classical limit when the ratio of the Compton wavelength of the black hole to its Schwarzschild radius vanishes. The region of strong gravity that develops when matter collapses to form the blackhole remains visible to the whole of spacetime and has to be described by a microscopic theory of strong gravity. The arguments imply that the information paradox is demoted from a paradox involving fundamental principles of physics to the problem of describing how matter at the highest densities gravitates.

Paper Structure

This paper contains 7 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Supremacy of quantum mechanics over geometry
  3. Horizon fluctuations effectively destroy the horizon
  4. Fluctuating horizon
  5. Fluctuations of a bifurcating Killing horizon
  6. Origin of information paradox
  7. Demotion of the information paradox to a status of a problem in strong gravity

Figures (1)

  • Figure 1: Penrose diagrams of blackhole spacetimes. Shown on the left is the standard diagram (evaporation is ignored). The shaded region is excluded. On the right, the diagram after inclusion of horizon quantum fluctuations is shown. The shaded region near $r=0$ depicts the strong gravity region.