Gravitating Scalars and Critical Collapse in the Large $D$ Limit

TL;DR

This paper develops a large $D$ limit approach to analyze scalar field collapse in general relativity, revealing critical phenomena and black hole formation in high-dimensional spacetimes.

Contribution

It introduces an analytical large $D$ framework for scalar collapse, providing new insights into horizon formation and critical scaling in high dimensions.

Findings

Analytical solutions for scalar fields in large $D$ limit.

Identification of critical amplitude leading to horizon formation.

Estimation of black hole size and Choptuik scaling exponent.

Abstract

We develop the large $D$ limit of general relativity for spherically symmetric scalar fields in both asymptotically flat and asymptotically anti-de Sitter spaces. The leading order equations in the $1/D$ expansion can be solved analytically, providing a large $D$ description of oscillating soliton stars. When the amplitude reaches a critical threshold, certain divergences occur which we interpret as signal of horizon formation. We estimate the size of the resulting black hole and obtain, with respect to that definition, a Choptuik scaling exponent for our family of solutions.