TeVeS gets caught on caustics

TL;DR

This paper analyzes the vector field dynamics in TeVeS theory, revealing that caustic singularities form generically, which challenges its classical viability, and suggests modifications to avoid these issues.

Contribution

It demonstrates that TeVeS's vector field develops caustic singularities generically, and proposes a modification to the kinetic terms to prevent this problem.

Findings

Vector fields in TeVeS form caustic singularities on gravitational timescales.

Singularity formation occurs both with and without matter.

Modifying the vector kinetic terms can potentially avoid singularities.

Abstract

TeVeS uses a dynamical vector field with timelike unit norm constraint to specify a preferred local frame. When matter moves slowly in this frame - the so-called quasi-static regime - Modified Newtonian Dynamics (MoND) results. Theories with such vectors (such as Einstein-aether) are prone to the vector dynamics forming singularities which render their classical evolution problematic. Here we analyse the dynamics of the vector in TeVeS in various situations. We find that, quite generically, the vector field develops caustic singularities on time scales of order the gravitational in-fall time. Having shown singularity formation is generic with or without matter, Bekenstein's original formulation of TeVeS appears dynamically problematic. We argue that by modifying the vector field kinetic terms to the more general form used by Einstein-Aether this problem may be avoided.