D. Grumiller, D. Mayerhofer
On Static Solutions in 2D Dilaton Gravity with Scalar Matter
Preprint series: ESI preprints

MSC:

83C57 Black holes

83C75 Space-time singularities, cosmic censorship, etc.

83E15 Kaluza-Klein and other higher-dimensional theories

PACS: 04.60.Kz,04.70.Bw,04.20.Dw
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.