Moving sources in a ghost condensate

TL;DR

This paper analyzes how ghost condensation, which spontaneously breaks Lorentz symmetry, alters gravity when the gravitating source is in motion. It extends the earlier static-potential analysis by computing the gravitational potential for a moving source, showing that for $v \gg v_s$ the Newtonian potential is recovered with negligible corrections at astrophysical scales, despite an underlying IR instability. The tachyonic, long-wavelength modes induce growth only near the region where the source passed and are not observable to fast-moving observers, but the vacuum instability still imposes an upper bound on the symmetry-breaking scale $M$ comparable to the static case. Consequently, observational signatures of this model are expected to be exotic astrophysical events rather than terrestrial gravity tests, unless a direct ghost–matter coupling is present. The work highlights a velocity-dependent phenomenology and motivates searches for unconventional gravitational phenomena consistent with ghost-condensate dynamics.

Abstract

Ghost condensation has been recently proposed as a mechanism inducing the spontaneous breaking of Lorentz symmetry. Corrections to the Newton potential generated by a static source have been computed: they yield a limit M < 10 MeV on the symmetry breaking scale, and - if the limit is saturated - they are maximal at a distance L ~ 1000 km from the source. However, these corrections propagate at a tiny velocity, v_s ~ 10^{-12} m/s, many orders of magnitude smaller than the velocity of any plausible source. We compute the gravitational potential taking the motion of the source into account: the standard Newton law is recovered in this case, with negligible corrections for any distance from the source up to astrophysical scales. Still, the vacuum of the theory is unstable, and requiring stability over the lifetime of the Universe gives a limit for M which is not too far from the one given above. In the absence of a direct coupling of the ghost to matter, signatures of this model will have to be searched in the form of exotic astrophysical events.