On static solutions in 2D dilaton gravity with scalar matter

TL;DR

This paper analyzes static solutions in 2D dilaton gravity with scalar matter, exploring conditions for black hole horizons, scalar hair existence, and generalizations including string theory, with a focus on global properties and dynamical system analysis.

Contribution

It provides a comprehensive analysis of static solutions, horizon conditions, and scalar hair in 2D dilaton gravity, including new insights into the role of the dynamical system's Jacobian and applications to string theory.

Findings

Killing horizons exist only if the Jacobian rank equals 3.

Asymptotically flat black holes with scalar hair can exist for certain self-interactions.

The paper includes an example relevant to general relativity and discusses generalizations to string theory.

Abstract

Within the first order formalism static solutions of generic dilaton gravity in 2D with self-interacting (scalar) matter can be discussed with ease. The question of (non)existence of Killing horizons is addressed and the interplay with asymptotic conditions is investigated. Naturally, such an analysis has to be a global one. A central element in the discussion is the rank of the Jacobi matrix of the underlying dynamical system. With some (pathological) exceptions Killing horizons exist only if it equals to 3. For certain self-interactions asymptotically flat black holes with scalar hair do exist. An example relevant to general relativity is provided. Finally, generalizations are addressed including 2D type 0A string theory as a particular example. Additionally, in a pedagogical appendix the mass definition in dilaton gravity is briefly reviewed and a unique prescription to fix scaling and shift ambiguity is presented.