Global solutions of a free boundary problem for selfgravitating scalar fields

TL;DR

This paper proves the global existence of solutions for a selfgravitating scalar field system with a free boundary, supporting the weak cosmic censorship hypothesis in a spherically symmetric setting.

Contribution

It establishes the first rigorous proof of global solutions with a null inner boundary outside the horizon for such systems.

Findings

Existence of spacetime with a null boundary outside the horizon

Global solutions extend to the exterior of an event horizon

Supports weak cosmic censorship hypothesis in spherical symmetry

Abstract

The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We study a selfgravitating spherically symmetric nonlinear scalar field. We show the global existence of a spacetime with a null inner boundary that initially is located outside the Schwarzschild radius or, more generally, outside an apparent horizon. The global existence of a patch of a spacetime that is exterior to an event horizon is obtained as a limiting case.