Self-gravitating stellar collapse: explicit geodesics and path integration

TL;DR

This paper derives explicit classical geodesics for stellar collapse and models quantum effects on particle wavefunctions, exploring quantum collapse possibilities beyond classical black hole formation.

Contribution

It extends classical collapse models by incorporating quantum effects through wavepacket path integration, providing new insights into quantum collapse scenarios.

Findings

Closed-form solutions for classical geodesics in Schwarzschild and Kruskal coordinates.

Wavefunction analysis showing ingoing and outgoing components during collapse.

Probabilistic modeling of star dispersion versus collapse into a black hole.

Abstract

We extend the work of Oppenheimer & Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r=2M.