Causality, shocks and instabilities in vector field models of Lorentz symmetry breaking

TL;DR

The paper analyzes vector-field models of Lorentz symmetry breaking in which a constrained vector $A_\mu$ models a dynamical ether via $A^2=l$ enforced by a Lagrange multiplier. It shows that in flat and curved spacetimes these models generically possess multiple characteristic surfaces, including a nonlinear mode with speed dependent on the ether configuration, and that certain backgrounds (notably $A_0=0$) render linear perturbation theory unstable and singular. The authors demonstrate shock formation in plane-symmetric configurations and prove that the classical Hamiltonian is not bounded from below, signaling severe stability and quantization challenges. They also discuss related model variants and argue that these pathologies persist under curvature couplings, casting doubt on the viability of such ether models for consistent Lorentz-violating physics. Overall, the work emphasizes that linearized analyses can be misleading and that the theories face fundamental dynamical and energetic difficulties across flat and curved spacetimes.

Abstract

We show that that vector field-based models of the ether generically do not have a Hamiltonian that is bounded from below in a flat spacetime. We also demonstrate that these models possess multiple light cones in flat or curved spacetime, and that the non-lightlike characteristic is associated with an ether degree of freedom that will tend to form shocks. Since the field equations (and propagation speed) of this mode is singular when the timelike component of the ether vector field vanishes, we demonstrate that linearized analyses about such configurations cannot be trusted to produce robust approximations to the theory.