# zbMATH — the first resource for mathematics

A solution-generating method in Einstein-scalar gravity. (English) Zbl 1429.83056
The authors of the article present a general method for constructing static, spherically symmetric solutions of $$(d + 2)$$-dimensional Einstein gravity minimally coupled to a real scalar field with a self-interacting potential. The whole solution is parametrised in terms of a single function, which encodes all the information about the local and global behaviour of the spacetime. The method gives integral formulas for the scalar field profile, the metric functions and the scalar potential. The authors have also given several applications of the solution-generating method, finding explicit solutions of Einstein-scalar gravity theory describing black holes, naked singularities and stars. A solution of interest has as a source a scalar field with the sine-Gordon solitonic profile. There are two points that the authors have not discussed in this paper and which must be supposed to a future investigation: the stability and the thermodynamical behaviour of the black-hole solutions.

##### MSC:
 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83C15 Exact solutions to problems in general relativity and gravitational theory 83C57 Black holes 83C75 Space-time singularities, cosmic censorship, etc. 35Q51 Soliton equations 85A15 Galactic and stellar structure
NP; NPspinor
Full Text: