Gravitational collapse and the Vlasov-Poisson system

TL;DR

This paper demonstrates that gravitational collapse of a pressureless fluid sphere can be closely approximated by global solutions of the Vlasov-Poisson system, linking collapse phenomena with kinetic theory models.

Contribution

It establishes a rigorous connection between gravitational collapse and the Vlasov-Poisson system, showing the latter can approximate collapse dynamics.

Findings

Collapse can be approximated by globally existing Vlasov-Poisson solutions

Vlasov-Poisson solutions can model finite-time gravitational collapse

Theoretical link between fluid collapse and kinetic equations

Abstract

A self-gravitating homogeneous ball of a fluid with pressure zero where the fluid particles are initially at rest collapses to a point in finite time. We prove that this gravitational collapse can be approximated arbitrarily closely by suitable solutions of the Vlasov-Poisson system which are known to exist globally in time.