Static and Dynamic Analysis of a Massless Scalar Field Coupled with a Class of Gravity Theories

TL;DR

This paper analytically derives static solutions for a massless scalar field coupled with a class of 2D gravity theories, explores black hole formation thresholds, and discusses their relation to phase transitions in gravitational collapse.

Contribution

It provides the first analytical solutions connecting various gravity models and demonstrates black hole formation thresholds in scalar field collapse.

Findings

Existence of black hole and naked singularity solutions.

Proof of no-hair theorem for these solutions.

Identification of a threshold for black hole formation in scalar collapse.

Abstract

General static solutions for a massless scalar field coupled to a class of effectively 2-d gravity theories continuously connecting spherically symmetric $d$-dimensional Einstein gravity ($d >3$) and the CGHS model are analytically obtained. They include black holes and point scalar charge solutions with naked singularities, and are used to give an analytic proof of no-hair theorem. Exact scattering solutions in $s$-wave 4-d Einstein gravity are constructed as a generalization of corresponding static solutions. They show the existence of black hole formation threshold for square pulse type incoming stress-energy flux, above which trapped surfaces are dynamically formed. The relationship between this behavior and the numerically studied phase transition in this system \cite{choptuik} is discussed.