Spherically symmetric Einstein-scalar-field equations for wave-like decaying null infinity

TL;DR

This paper proves the existence and uniqueness of solutions to spherically symmetric Einstein-scalar-field equations with wave-like decaying initial data at null infinity, extending Christodoulou's results and emphasizing the sharpness of decay conditions.

Contribution

It establishes local and global existence and uniqueness for small initial data, generalizes Christodoulou's solutions, and highlights the optimal decay conditions.

Findings

Unique local solutions for initial data

Unique global solutions for small initial data

Generalization of Christodoulou's solutions

Abstract

We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's global generalized solutions to the wave-like decaying initial data. We emphasize that this decaying condition is sharp.