Gravitational waves in bimetric MOND

TL;DR

This paper analyzes the weak field limit of bimetric MOND, revealing its unique properties, including two sectors with distinct behaviors, and demonstrating solutions involving harmonic gravitational wave packets.

Contribution

It provides a detailed examination of the weak field limit of BIMOND, highlighting the differences from other bimetric theories and identifying solutions involving gravitational wave packets.

Findings

Hmn+ sector matches general relativity's WFL and has vacuum gravitational waves.

Hmn- sector is fully nonlinear and lacks gauge freedom.

Harmonic GR wave packets are solutions in the BIMOND WFL.

Abstract

I consider the weak field limit (WFL) of bimetric MOND (BIMOND): the lowest order in the small departures Hmn and H'mn from double Minkowski space-time. In particular, I look at propagating solutions, for a favorite subclass of BIMOND. The WFL splits into two sectors for two linear combinations, Hmn+ and Hmn-, of Hmn and H'mn. The Hmn+ sector is equivalent to the WFL of general relativity (GR), with its gauge freedom, and has the same vacuum gravitational waves. The Hmn- sector is fully nonlinear even for the weakest Hmn-, and inherits none of the coordinate gauge freedom. The equations of motion are scale invariant in the deep-MOND limit of purely gravitational systems. In these last two regards, the BIMOND WFL is greatly different from that of other bimetric theories studied to date. Despite the strong nonlinearity, an arbitrary pair of harmonic GR wave packets of Hmn and H'mn moving in the same direction, is a solution of the (vacuum) BIMOND WFL.