Surplus angle and sign-flipped Coulomb force in projectable Horava-Lifshitz gravity

Abstract

We obtain the static spherically symmetric vacuum solutions of Horava-Lifshitz gravity theory, imposing the detailed balance condition only in the UV limit. We find the solutions in two different coordinate systems, the Painleve-Gullstrand coordinates and the Poincare coordinates, to examine the consequences of imposing the projectability condition. The solutions in two coordinate systems are distinct due to the nonrelativistic nature of the Horava-Lifshitz gravity. In the Painleve-Gullstrand coordinates compiling with the projectability condition, the solution involves an additional integration constant which yields surplus angle and implies attractive Coulomb force between same charges.