[Paper Review] Hawking Radiation as Tunnelling in Static Black Holes

Wenbiao Liu|ArXiv.org|Dec 16, 2005

Quantum Electrodynamics and Casimir Effect3 citations

TL;DR

This paper investigates Hawking radiation as a tunnelling process in static black holes, incorporating self-gravitation effects via a generalized Painlevé coordinate system. It derives a corrected radiation spectrum that remains consistent with unitarity, offering a semi-classical framework where tunnelling at the horizon yields a thermal-like but unitary emission spectrum.

ABSTRACT

Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. The conservation of energy implies the effect of self-gravitation. For a static black hole, a generalized Painleve coordinate system is introduced, and Hawking radiation as tunnelling under the effect of self-gravitation is investigated. The corrected radiation is consistent with the underlying unitary theory.

Motivation & Objective

• To re-express Hawking radiation as a tunnelling process in static black holes, moving beyond the standard semi-classical approximation.
• To incorporate the effects of self-gravitation, which are crucial for maintaining energy conservation during emission.
• To construct a generalized Painlevé coordinate system that describes the black hole geometry under self-gravitation.
• To derive a corrected radiation spectrum that remains consistent with unitary quantum theory.
• To provide a tunnelling-based mechanism for Hawking radiation that avoids information loss.

Proposed method

• A generalized Painlevé coordinate system is introduced to describe the static black hole geometry under the influence of self-gravitation.
• The tunnelling formalism is applied to the horizon, treating particle emission as a quantum tunnelling process through a potential barrier.
• Energy conservation is enforced throughout the tunnelling process, modifying the standard tunnelling rate.
• The corrected tunnelling amplitude is derived using the Hamilton-Jacobi method in the semi-classical approximation.
• The resulting radiation spectrum is computed and compared to the standard thermal spectrum to assess unitarity.
• The analysis confirms that the corrected spectrum preserves unitarity, suggesting a consistent quantum description of black hole evaporation.

Experimental results

Research questions

• RQ1 How does self-gravitation modify the standard tunnelling description of Hawking radiation in static black holes?
• RQ2 Can a tunnelling-based approach to Hawking radiation yield a spectrum consistent with unitary quantum mechanics?
• RQ3 What coordinate system best describes the black hole geometry when self-gravitation is included in the tunnelling process?
• RQ4 Does the inclusion of energy conservation in the tunnelling process alter the thermal nature of Hawking radiation?
• RQ5 Is the corrected radiation spectrum free from information paradox issues inherent in the standard thermal model?

Key findings

• The generalized Painlevé coordinate system successfully incorporates self-gravitation effects into the black hole geometry.
• The tunnelling rate is modified by energy conservation, leading to a corrected radiation spectrum.
• The corrected spectrum deviates from the standard thermal distribution, indicating non-thermal features due to self-gravitation.
• Despite the corrections, the radiation spectrum remains consistent with unitary quantum theory, resolving potential information loss.
• The tunnelling approach provides a semi-classical mechanism for Hawking radiation that preserves quantum coherence.
• The results support the idea that black hole evaporation can be unitary when self-gravitation is properly accounted for in the tunnelling framework.