[Paper Review] On the nature of black hole information from unitarity

van Putten, H P M Maurice|arXiv (Cornell University)|Jun 25, 2015

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes that the information content of a black hole is conserved via a new conserved quantity, I = 4πEM, derived from the unitary emission of photons during evaporation. By modeling observers undergoing discrete velocity jumps during photon emission, the authors identify I as the underlying conserved quantity that explains the no-hair theorem's persistence throughout evaporation, preserving information in macroscopic black holes.

ABSTRACT

We identify the astronomically long evaporative lifetimes $t_{ev}$ of macroscopic black holes with unitary evolution in photon emissions one-by-one. To study the nature of black hole information, we consider observers ${\cal O}$ of mass-energy $E$, experiencing discrete transitions in space-time with each photon emission. From the associated jumps in their velocity four-vector, we derive an integral of motion $EM$, where $M=M(t)$ denotes the mass of the black hole. $I=4\pi EM$ was recently identified with the information localizing $E$ at the center of a sphere of radius $2M$. We here identify $I$ as a new conserved quantity underlying the no-hair theorem during black hole evaporation.

Motivation & Objective

• To understand how information is preserved during black hole evaporation under unitary quantum evolution.
• To resolve the black hole information paradox by identifying a conserved quantity that maintains the no-hair theorem during evaporation.
• To connect the long evaporative lifetime of macroscopic black holes with discrete, unitary photon emissions.

Proposed method

• Model observers with mass-energy E experiencing discrete velocity four-vector jumps during each photon emission.
• Derive an integral of motion EM, where M(t) is the time-dependent black hole mass.
• Identify I = 4πEM as a conserved quantity linked to information localization at the black hole center within a sphere of radius 2M.
• Use the structure of unitary evolution in photon emissions to derive the conservation of I during the evaporation process.
• Relate I to the no-hair theorem by showing it remains invariant despite mass loss and radiation emission.
• Establish that I encodes the information content of the observer's energy E localized at the black hole's center.

Experimental results

Research questions

• RQ1 How can information be conserved during black hole evaporation if the process is unitary and the black hole loses mass?
• RQ2 What conserved quantity underlies the persistence of the no-hair theorem during the entire evaporation process?
• RQ3 How is the information content of an observer's energy E localized at the black hole center related to the evaporation dynamics?
• RQ4 Can the astronomically long evaporation timescale be reconciled with discrete, unitary photon emissions?
• RQ5 What is the physical and mathematical role of the quantity I = 4πEM in preserving information?

Key findings

• The quantity I = 4πEM is identified as a new conserved quantity during black hole evaporation, arising from unitary photon emission and velocity jumps in observers.
• This conserved quantity I explains the persistence of the no-hair theorem even as the black hole loses mass and emits radiation.
• Information associated with an observer's energy E is localized at the black hole center within a sphere of radius 2M, encoded in the conserved I.
• The derivation links the long evaporation timescale t_ev to discrete, unitary transitions in space-time, preserving quantum coherence.
• The conserved I provides a mechanism for information retention that avoids the information paradox by maintaining unitarity.
• The result establishes a direct connection between the observer's energy, black hole mass, and the conservation of information via I = 4πEM.