TeVeS gets caught on caustics

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 quasistatic regime--modified Newtonian dynamics results. Theories with such vectors (such as Einstein-Aether) are prone to the vector dynamics forming singularities that render their classical evolution problematic. Here, we analyze the dynamics of the vector in TeVeS in various situations. We begin by analytically showing that the vacuum solution of TeVeS forms caustic singularities under a large class of physically reasonably initial perturbations. This shows the classical evolution of TeVeS appears problematic in the absence of matter. We then consider matter by investigating black hole solutions. We find large classes of new black hole solutions with static geometries, where the curves generated by the vector field are attracted to the black hole and may form caustics. We go on to consider the full dynamics with matter by numerically simulating, assuming spherical symmetry, the gravitational collapse of a scalar, and the evolution of an initially nearly static boson star. We find that in both cases our initial data evolves so that the vector field develops caustic singularities on a time scale 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.