Back-reaction of the Hawking radiation flux on a gravitationally collapsing star II

Abstract: A star collapsing gravitationally into a black hole emits a flux of radiation, known as Hawking radiation. When the initial state of a quantum field on the background of the star, is placed in the Unruh vacuum in the far past, then in the exterior Hawking radiation corresponds to a flux of positive energy radiation travelling outwards from near the surface to future infinity. Based on pair creation, the evaporation of the collapsing star can be equivalently described by the absorption of an ingoing negative energy flux of radiation travelling towards the center of the star. Here, we are interested in the evolution of the star during its collapse. Thus we include the backreaction of the negative energy Hawking flux in the interior geometry of the collapsing star when writing the full 4-dimensional Einstein and hydrodynamic equations. Hawking radiation emitted before the star passes through its Schwarzschild radius slows down and reverses the collapse of the star. The star evaporates without forming an horizon or a singularity. This study provides a more realistic investigation than the one first presented in [1], since the backreaction of Hawking radiation flux on the collapsing star is studied in the case when the initial state of the field is in Unruh's vacuum.

• The paper demonstrates that Hawking radiation’s negative energy flux decelerates and reverses stellar collapse to prevent event horizon formation.
• The paper employs a four-dimensional treatment of Einstein and hydrodynamical equations to detail peak luminosity as the star nears its Schwarzschild radius.
• The paper reveals a universal collapse behavior across varied initial conditions, offering insights that may resolve the black hole information paradox.

Back-reaction of the Hawking Radiation Flux on a Gravitationally Collapsing Star

The research paper discusses the impact of Hawking radiation on the collapse of a star, utilizing a framework where the initial quantum field conditions are placed in Unruh’s vacuum. Unlike prior approximations that considered idealistic setups, the paper incorporates a more physically realistic scenario by accounting for the backreaction of Hawking radiation. This paper contributes to the ongoing investigation into one of the pivotal problems in quantum gravity—understanding the evolution of quantum fields on a collapsing star.

Summary of Findings

The core of the paper revolves around modeling the quantum mechanical backreaction of Hawking radiation flux as a star undergoes gravitational collapse. The study specifically addresses the dynamics of such a star by incorporating the negative energy flux of Hawking radiation into the equations governing the star's collapse. The paradigm shifts from traditional scenarios of black hole formation by suggesting that Hawking radiation, occurring during the pre-collapse phase, induces significant alterations in the collapse trajectory of a star.

The analysis employs a fully four-dimensional treatment of Einstein's equations alongside hydrodynamical equations to model the star’s collapse. Key modifications include rendering the star inhomogeneous and introducing a Hawking radiation flux characterized by ingoing negative energy and outgoing positive energy components.

Key Results

1. Inhibition of Event Horizon Formation: The study's computational results demonstrate that Hawking radiation decelerates and subsequently halts the collapse of the star. The backreaction prevents the establishment of an event horizon or a singularity, culminating instead in a stellar rebounce.
2. Luminosity Dynamics: As the star approaches what would traditionally be its Schwarzschild radius, the Hawking radiation becomes increasingly significant. The luminosity reaches a peak—a critical point before the reversal of collapse—without crossing the event horizon.
3. Universal Behavior Across Parameters: Numerical simulations indicate a universal behavior of stellar collapse dynamics, showing consistent outcomes across various initial star masses and radii. The time it takes for a star to reach maximum Hawking luminosity seems largely independent of its initial conditions.

Implications

The implications of this research are profound, potentially altering the current understanding of black hole physics. If gravitational collapse does not culminate in a singularity or event horizon but instead results in a rebounding star, this would offer a resolution to the famed information paradox. The absence of event horizons invites reconsideration of various long-held assumptions in general relativity and quantum mechanics, particularly the irreversible loss of information in black holes.

This work diminishes the inevitability of black hole formation and suggests a pathway where quantum mechanics influence classical gravitational phenomena significantly, preventing singularity and horizon formation altogether.

Future Directions

Further exploration of this theoretical framework and the exact dynamics of Hawking radiation's backreaction could yield methods to track post-bounce evolution. Sophisticated numerical and analytical techniques could refine these results, potentially providing empirical observables to distinguish between conventional black holes and those impacted by quantum mechanical effects.

Moreover, these insights encourage the examination of other potential vacuum states or variations in initial conditions' impact on similar astrophysical processes. This could pave the path for discovering new quantum phenomena in gravitational systems.

Overall, this study opens a compelling narrative for the intersection of quantum mechanics and general relativity, seeking an improved understanding of black hole physics, an endeavor that continues to challenge and intrigue theoretical physicists worldwide.