# The point-particle solution and the asymptotic flatness in 2+1 Horava gravity

## TL;DR

This paper demonstrates that the point-particle solution in 2+1 nonprojectable Horava gravity is identical to that in 2+1 General Relativity, leading to similar asymptotic flatness conditions and energy definitions.

## Contribution

It establishes the equivalence of point-particle solutions in 2+1 Horava gravity and General Relativity, and adapts the asymptotic flatness condition accordingly.

## Key findings

- Point-particle solutions are identical in both theories.
- Asymptotic flatness condition is the same as in GR.
- Energy expressions are equivalent, with minor coupling differences.

## Abstract

We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Horava is exactly the same as its analogous in 2+1 General Relativity. This solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Horava theory to a point particle with relativistic action. As a consequence of this result, we define the condition of asymptotic flatness exactly in the same way of 2+1 General Relativity. A remarkable feature of this condition is that the dominant mode is not fixed, but affected by the mass of the configuration. Anoter important coincidence with 2+1 General Relativity under asymptotic flatness is that the energy is the same (except for some coupling constants involved), the z = 1 term with the derivative of the lapse function does not contribute.