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.Comment: Latex file, 18 pages. To fit published versio
