# Attractors of the Einstein-Klein Gordon system

## TL;DR

This paper demonstrates that negative Einstein metrics serve as attractors in the Einstein-Klein-Gordon system, employing an improved technique involving energy density correction for better control of matter fields.

## Contribution

It introduces a novel method that combines a correction to the energy density with continuity equations to analyze attractors in the Einstein-Klein-Gordon system.

## Key findings

- Negative Einstein metrics are attractors in the system
- Enhanced control of matter fields via energy density correction
- Improved analytical techniques for Einstein-Klein-Gordon dynamics

## Abstract

It is shown that negative Einstein metrics are attractors of the Einstein-Klein-Gordon system. As an essential part of the proof we upgrade a technique that uses the continuity equation complementary to $L^2$-estimates to control massive matter fields. In contrast to earlier applications of this idea we require a correction to the energy density to obtain sufficiently good pointwise bounds.