Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory

TL;DR

This paper explores the 2+1 nonprojectable Horava gravity at its critical point, revealing it has no local degrees of freedom but admits nonflat solutions, challenging traditional notions of curvature and Newtonian potential in such theories.

Contribution

It demonstrates that at the critical point, the 2+1 Horava theory admits nonflat solutions despite lacking local degrees of freedom, highlighting unique geometric properties.

Findings

Existence of nonflat, non-asymptotically flat solutions

Absence of Newtonian potential in the theory

Restriction to flat solutions among asymptotically flat geometries

Abstract

We present the interesting case of the 2+1 nonprojectable Horava theory formulated at the critical point, where it does not posses local degrees of freedom. The critical point is defined by the value of a coupling constant of the theory. We discuss how, in spite of the absence of degrees of freedom, the theory admits solutions with nonflat or nonconstant curvature. We consider the theory without cosmological constant and without terms of higher order derivatives, hence this is an effect that can be seen at the same order of 2+1 general relativity. We present an exact nonflat solution that is not asymptotically flat. The presence of solutions with nontrivial curvature seems to be related to the relaxing of the asymptotically flat condition. We discuss that there is no analogue of Newtonian potential in this theory, and a broad class of asymptotically flat geometries leads to the restriction that the only solutions that can be found among them are the flat ones.