Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory

TL;DR

This paper investigates the asymptotic flatness and solutions of the critical 2+1 dimensional Horava gravity, revealing both similarities and differences with 2+1 general relativity, including the absence of local degrees of freedom and existence of nonflat solutions.

Contribution

It provides a detailed analysis of asymptotically flat solutions in critical 2+1 Horava gravity and compares them with 2+1 general relativity, highlighting new nonflat solutions.

Findings

Regular asymptotically flat solutions are totally flat.

The theory has no local degrees of freedom.

An exact nonflat solution exists outside the asymptotically flat class.

Abstract

The Horava theory in 2+1 dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with 2+1 general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on this relationship, we study the asymptotically flat solutions of the effective action. We take the general definition of asymptotic flatness from 2+1 general relativity, where an asymptotically flat region with a nonfixed conical angle is approached. We show that a class of regular asymptotically flat solutions are totally flat. The class is characterized by having nonnegative energy (when the coupling constant of the Ricci scalar is positive). We present a detailed canonical analysis on the effective action showing that the dynamics of the theory forbids local degrees of freedom. Another similarity with 2+1 general relativity is the absence of a Newtonian force. In contrast to these results, we find evidence against the similarity with 2+1 general relativity: we find an exact nonflat solution of the same effective theory. This solution is out of the set of asymptotically flat solutions.