Global Non-Linearly Stable Large-Data Solutions to the Einstein Scalar Field System

TL;DR

This paper constructs and analyzes large-data solutions to the Einstein scalar field system, demonstrating their global stability and providing bounds on derivatives, extending prior results in spherical symmetry.

Contribution

It introduces new bounds for higher derivatives of solutions and constructs a class of globally stable, large-data solutions beyond spherical symmetry.

Findings

Existence of large-data, globally nonlinearly stable solutions.

New bounds controlling higher derivatives of metric and scalar field.

Construction of generalized wave-coordinates for stability analysis.

Abstract

I study a class of global, causal geodesically complete solutions to the spherically symmetric Einstein scalar field (SSESF) system . Extending results of Luk-Oh (Quantitative Decay Rates for Dispersive Solutions to the Einstein-Scalar Field System in Spherical Symmetry, arXiv:1402.2984), Luk-Oh-Yang (Solutions to the Einstein-Scalar-Field System in Spherical Symmetry with Large Bounded Variation Norms, arXiv:1605.03893), I provide new bounds controlling higher derivatives of both the metric components of the solution and the scalar field itself for large data solutions to SSESF. Moreover, by constructing a particular set of generalized wave-coordinates, I show that, assuming sufficient regularity of the data, these solutions are globally non-linearly stable to non-spherically symmetric perturbations by recent results of Luk and Oh. In particular, I demonstrate the existence of a large collection of non-trivial examples of large data, globally nonlinearly stable, dispersive solutions to the Einstein scalar field system.