Surplus Angle and Sign-flipped Coulomb Force in Projectable Horava-Lifshitz Gravity

TL;DR

This paper derives static vacuum solutions in projectable Horava-Lifshitz gravity, revealing a surplus angle and a sign-flipped Coulomb force, highlighting the theory's non-relativistic effects and coordinate-dependent solutions.

Contribution

It provides the first detailed analysis of vacuum solutions in projectable HL gravity in different coordinate systems, emphasizing the impact of the projectability condition.

Findings

Surplus angle in the spacetime geometry.

Sign-flipped Coulomb force between charges.

Distinct solutions in different coordinate systems.

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 Painlev\'e-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 non-relativistic nature of the HL gravity. In the Painleve-Gullstrand coordinates complying with the projectability condition, the solution involves an additional integration constant which yields surplus angle and implies attractive Coulomb force between same charges.