Static, spherically symmetric solutions with a scalar field in Rastall gravity

TL;DR

This paper explores static, spherically symmetric solutions in Rastall gravity coupled with scalar fields, revealing new exact solutions, including wormholes and black holes, and establishing connections with GR solutions and k-essence theories.

Contribution

It introduces new exact solutions in Rastall gravity with scalar fields, linking them to known GR and k-essence solutions, and analyzes their properties.

Findings

Discovery of new solutions with scalar fields in Rastall gravity.

Identification of solutions matching GR and k-essence geometries.

Potential for wormholes and regular black holes within Rastall framework.

Abstract

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter $a$. Some of these solutions describe the same space-time geometry as the recently found solutions in the $k$-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter $a$. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.