On the space of solutions of the Horava theory at the kinetic-conformal point

Abstract

The nonprojectable Horava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multupliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.

v3: Eqs. (2.7), (3.9) and (3.10) have been corrected, with no consequences on the main results. Some references added, some typos corrected

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• Dynamics of the anisotropic conformal Horava theory versus its kinetic-conformal formulation
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Phenomenologically viable gravitational theory based on a preferred foliation without extra modes