Static Spherically Symmetric Solutions to modified Horava-Lifshitz Gravity with Projectability Condition

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In this paper we seek static spherically symmetric solutions of Horava-Lifshitz-like gravity with projectability condition.

• We consider the most general form of gravity action without detailed balance, and require the spacetime metric to respect the projectability condition.
• We find that for any value of $\lambda$, it may exists the solutions of topology $R\times M_3$, where $R$ is the time direction and $M_3$ is a three-dimensional maximally symmetric space depending on the value of cosmological constant and the potential of the action.
• Besides, in the UV region where $\lambda\neq 1$, we find Minkowski or de-Sitter space-time as the solution, while in the IR region where $\lambda=1$, we prove that (dS-)Schwarzschild solution is the only nontrivial solution.