Analytic discrete self-similar solutions of Einstein-Klein-Gordon at large D

TL;DR

This paper analytically constructs an infinite family of discretely self-similar solutions for the Einstein-massless-Klein-Gordon system using large-D expansion, enhancing understanding of critical gravitational collapse.

Contribution

It provides the first closed-form analytic solutions for discretely self-similar critical solutions in Einstein-Klein-Gordon systems at large D.

Findings

Constructed analytic solutions in closed form

Identified universal features of solutions

Compared large-D solutions with finite-D numerical results

Abstract

Discretely self-similar solutions govern critical gravitational collapse and have been known only numerically since Choptuik's pioneering work. We construct, in closed analytic form, an infinite family of such solutions of the Einstein-massless-Klein-Gordon system using the large-D expansion. We characterize their structure and compare them with numerical critical solutions at finite D, identifying both universal features and distinctly large-D behavior.