Abstract
In this paper, we first study spherically symmetric, stationary vacuum configurations in general covariant theory [ extension] of Hořava-Lifshitz gravity with the projectability condition and an arbitrary value of the coupling constant . We obtain all the solutions with the assumed symmetry in closed forms. If the gauge field and the Newtonian prepotential do not directly couple to matter fields, the theory is inconsistent with solar system tests for , no matter how small is. This is shown to be true also with the most general ansatz of spherically symmetric (but not necessarily stationary) configurations. Therefore, to be consistent with observations, one needs either to find a mechanism to restrict precisely to its relativistic value , or to consider and/or as parts of the four-dimensional metric on which matter fields propagate. In the latter, requiring that the line element be invariant not only under the foliation-preserving diffeomorphism but also under the local transformations, we propose the replacements, and , where is a dimensionless coupling constant to be constrained by observations, and are, respectively, the lapse function and shift vector, and . With this prescription, we show explicitly that the aforementioned solutions are consistent with solar system tests for both and , provided that . From this result, the physical and geometrical interpretations of the fields and become clear. However, it still remains to be understood how to obtain such a prescription from the action principle.
- Received 16 June 2012
DOI:https://doi.org/10.1103/PhysRevD.86.104024
© 2012 American Physical Society