[Paper Review] The black hole information paradox

Steven B. Giddings|ArXiv.org|Aug 28, 1995

Black Holes and Theoretical Physics26 references61 citations

TL;DR

This paper investigates the black hole information paradox, arguing that if black hole remnants exist, they would imply an infinite number of internal quantum states in Reissner-Nordström black holes, leading to an unphysical infinite production rate in background fields. The core contribution is a refutation of remnants as a resolution, suggesting instead that unitarity and causality cannot both hold unless locality or quantum mechanics breaks down.

ABSTRACT

A concise survey of the black hole information paradox and its current status is given. A summary is also given of recent arguments against remnants. The assumptions underlying remnants, namely unitarity and causality, would imply that Reissner Nordstrom black holes have infinite internal states. These can be argued to lead to an unacceptable infinite production rate of such black holes in background fields. (To appear in the proceedings of the PASCOS symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995).

Motivation & Objective

• To analyze the black hole information paradox arising from Hawking radiation's apparent loss of quantum information.
• To challenge the viability of black hole remnants as a resolution by showing they imply unphysical infinite production rates.
• To explore the tension between unitarity, causality, and energy conservation in quantum gravity.
• To assess whether non-locality or modified locality in quantum gravity could resolve the paradox.
• To evaluate the consistency of remnants with quantum field theory in curved spacetime and effective field theory constraints.

Proposed method

• Uses effective field theory and Euclidean path integral methods to compute the rate of black hole pair production.
• Applies the Gibbons-Hawking partition function formalism to relate black hole entropy to the partition function of thermal gravity.
• Analyzes the behavior of the functional integral over near-horizon geometries, particularly in the limit of small charge-to-field ratio (QB ≪ 1).
• Examines the role of infinite internal states in Reissner-Nordström black holes and their implications for vacuum stability.
• Uses Penrose diagrams to visualize causal structure and non-local signaling in Hawking radiation.
• Considers the thermodynamic and quantum gravitational consequences of infinite state degeneracy in black hole configurations.

Experimental results

Research questions

• RQ1 Does the existence of black hole remnants lead to an unphysical infinite production rate of such objects in background fields?
• RQ2 Can unitarity and causality coexist if remnants are assumed to store information?
• RQ3 What are the quantum gravitational consequences of an infinite number of internal states in charged black holes?
• RQ4 Is the information loss in Hawking radiation consistent with energy conservation, and what are the implications for effective field theory?
• RQ5 Can non-locality in quantum gravity resolve the information paradox without violating causality or unitarity?

Key findings

• The assumption of remnants leads to an infinite number of internal quantum states in Reissner-Nordström black holes, which implies an unphysical infinite production rate in external fields.
• This infinite production rate arises because the Euclidean path integral over near-horizon geometries yields a divergent rate when the action of configurations is of order one, even for small QB.
• The analysis confirms that infinite state degeneracy leads to Γ = ∞ × e^{-πQ/B}, implying a divergent pair production rate.
• The result contradicts experimental observations, suggesting that remnants cannot be a viable resolution to the information paradox.
• The paper concludes that either unitarity or causality must fail in the presence of remnants, undermining their role as a solution.
• The paradox remains unresolved, but the evidence points toward a breakdown of locality or quantum mechanics, with non-locality in string theory as a possible resolution.