On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates

TL;DR

This paper establishes improved criteria for the global existence of classical solutions to the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates, preventing finite-time blow-up.

Contribution

It introduces new continuation criteria and additional conditions that ensure solutions exist globally without singularities.

Findings

Improved continuation criterion for global solutions

Additional criteria preventing finite-time blow-up

Enhanced understanding of solution behavior in Einstein-Vlasov system

Abstract

The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e. polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other types of criteria which prevent finite time blow-up are also given.