[Paper Review] Naked singularities and quantum gravity - interpreting the quantum divergence in spherical collapse

Tomohiro Harada, Hideo Iguchi+4 more|arXiv (Cornell University)|Oct 27, 2000

Quantum Mechanics and Applications3 citations

TL;DR

This paper interprets the divergence of quantum flux in scalar field emission during spherical dust collapse toward a naked singularity as a breakdown of the semiclassical approximation, not a physical divergence. It shows that quantum gravity effects become dominant one Planck time before singularity formation, with total emitted energy capped at one Planck unit, implying that only full quantum gravity can determine whether the system radiates away or forms a black hole.

ABSTRACT

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. In this paper we provide an interpretation for this divergence, using the naked singularity in dust collapse. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state. We also calculate the spectrum of the produced particles for the self-similar dust model.

Motivation & Objective

• To interpret the divergence of outgoing quantum flux in scalar field emission during spherical collapse toward a naked singularity.
• To determine the validity limits of the semiclassical approximation in quantum field theory on classical curved backgrounds.
• To assess whether quantum gravity effects become dominant before or after singularity formation in dust collapse models.
• To evaluate whether the final state of the collapsing star is a radiating remnant or a black hole, based on quantum gravitational dynamics.

Proposed method

• Analyzing the semiclassical approximation in the context of a self-similar dust collapse model with a naked shell-focusing singularity.
• Calculating the outgoing quantum flux of a massless scalar field on the classical background of the collapsing star.
• Identifying the epoch at which curvature reaches the Planck scale as the point where the semiclassical approximation breaks down.
• Estimating the total emitted energy during the valid phase of the semiclassical approximation, finding it to be approximately one Planck unit.
• Assessing the role of back-reaction under classical gravity, concluding it does not dominate before the Planck time threshold.
• Computing the particle production spectrum for the self-similar dust model to analyze quantum emission characteristics.

Experimental results

Research questions

• RQ1 At what point does the semiclassical approximation fail during the collapse leading to a naked singularity?
• RQ2 What is the total energy emitted via quantum flux before the semiclassical approximation breaks down?
• RQ3 Does back-reaction become significant before the Planck-scale curvature is reached in the collapsing core?
• RQ4 Can the final fate of the collapsing star—radiation or black hole formation—be determined without quantum gravity?
• RQ5 What is the spectrum of particles produced during the collapse in the self-similar dust model?

Key findings

• The semiclassical approximation breaks down approximately one Planck time before naked singularity formation due to curvature reaching the Planck scale.
• The total energy emitted during the valid phase of the semiclassical approximation is bounded at roughly one Planck unit, indicating no divergence in physical emission.
• Back-reaction effects do not become significant while gravity remains classical, implying the breakdown is due to curvature, not quantum corrections.
• The divergence in quantum flux observed in semiclassical calculations is an artifact of the approximation's failure, not a physical signal.
• The particle production spectrum in the self-similar dust model is calculable and provides a signature of quantum emission prior to the Planck epoch.
• The final evolution of the star—whether it radiates away or forms a black hole—cannot be determined without a full theory of quantum gravity.