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arXiv · 1606.06242

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

K. A. Bronnikov·J. C. Fabris·O. F. Piattella·E. C. Santos
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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.

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K. A. Bronnikov, J. C. Fabris, O. F. Piattella, E. C. Santos. 2016-06-20. Static, spherically symmetric solutions with a scalar field in Rastall gravity. https://doi.org/10.1007/s10714-016-2152-0

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