Unitary Black Hole Evaporation Achieves Page Curve Reproduction at Half Mass Loss

The evaporation of black holes presents a long-standing problem in theoretical physics, challenging our understanding of quantum mechanics and gravity. Paul M. Alsing, from Florida Atlantic University, alongside colleagues, now proposes novel models inspired by quantum optics to address this complex phenomenon. Their research focuses on creating operationally simple frameworks that maintain the thermal characteristics of Hawking radiation and, crucially, attempt to reproduce the Page Curve , a theoretical prediction indicating information escapes a black hole as it evaporates. By modelling black holes as squeezed states interacting with vacuum modes, the team utilises a symplectic formalism to trace the evolution of entanglement between the black hole and emitted radiation, offering new insights into the preservation of information during black hole evaporation. This work represents a significant step towards resolving the information paradox and furthering our comprehension of quantum gravity.

Thermofield Double State and Hawking Radiation Analysis

Hawking’s work on black hole evaporation continues to be a crucial area of research, particularly concerning the black hole information problem, which arises from the contradiction between quantum mechanics’ requirement for unitarity and the thermal nature of Hawking radiation. The standard model suggests that a pure quantum state entering a black hole evolves into thermal Hawking radiation upon complete evaporation, violating unitarity. Researchers examine the thermofield double state to investigate this, describing the entangled vacuum state and analysing the reduced quantum state of Hawking radiation by tracing out causally disconnected regions. This analysis compares the von Neumann entropy with the Bekenstein-Hawking entropy, establishing a maximum limit for the former, and identifies the Page time, when the black hole has emitted approximately half its mass.

At this time, the area of the black hole shrinks, and the von Neumann entropy approaches the Bekenstein-Hawking entropy, potentially resolving the information paradox. This necessitates a “turnover” in the generalized entropy, combining the Bekenstein-Hawking entropy with the entropy of external radiation and other quantum fields, linked to the point where the Hilbert space dimension of the black hole equals that of the external radiation. The calculations aim to establish correlations between the black hole’s behaviour at early and late stages of evaporation, suggesting a pathway towards a unitary theory and preservation of quantum information.

Hawking Radiation and Black Hole Entanglement Dynamics

Scientists have developed models for unitary black hole evaporation, concentrating on approaches that preserve the thermal nature of emitted Hawking Radiation. The research models black holes as single mode squeezed states interacting with vacuum modes, generating entangled pairs representing Hawking Radiation and its internal partner particle. Through a symplectic formalism, the team tracked the evolution of these systems by monitoring the means and variances of quadrature operators, allowing precise measurement of correlations and entanglement. Experiments revealed that modifications to the entanglement between the black hole and its Hawking partner particles support a mechanism for microscopic wormholes, arising from the quantum entanglement of the black hole’s interior and exterior.

Measurements confirm a reduction in entanglement entropy as the system returns to a pure state, aligning with the theoretical framework of Euclidean path integrals and semi-classical approximations. The study leverages the analogy between a thermofield double state and the two-mode squeezed vacuum state, modelling the black hole as an effective “pump laser”, and achieved a Page curve by exploring analytical and perturbative approaches. Initial measurements show the black hole begins in a pure quantum state, while the Hawking Radiation starts in a vacuum state, and as the black hole evaporates, the Hilbert spaces of both systems become nearly equal at the Page time, indicating peak entanglement.

Simulating Black Hole Evaporation with Gaussian Models

This research introduces Gaussian models to simulate unitary black hole evaporation, addressing a long-standing problem in theoretical physics. By representing the black hole as a squeezed state interacting with vacuum modes, the authors developed a symplectic formalism to track the evolution of entanglement and correlations between the black hole and emitted Hawking radiation. Through this approach, they successfully generated Page curves under reasonable assumptions regarding reflectivity within the model. The significance of this work lies in providing operationally simple models that approximately preserve the thermal characteristics of Hawking radiation while demonstrating a mechanism for information recovery, aligning with the principles of unitarity.

Calculations of purity and logarithmic negativity further quantified the correlations between the black hole at different stages of evaporation, offering insights into the dynamics of information transfer. While acknowledging limitations stemming from the Gaussian nature of their states, the authors suggest future research could explore extensions beyond Gaussian states to incorporate more realistic physical scenarios and investigate the impact of different reflectivity profiles on the Page curve and entanglement measures. These models represent a step towards a more complete understanding of black hole evaporation and the preservation of quantum information in extreme gravitational environments.