Mechanism for Restoring Lorentz Symmetry in the Gravitational Sector

Establish a concrete dynamical mechanism by which Lorentz invariance is restored in the gravitational sector of Hořava–Lifshitz/khronometric (Einstein-Æther) gravity at low energies, ensuring that the æther effectively decouples and the relativistic causal structure reappears so that detector dynamics reduce to the standard relativistic Unruh limit.

Background

The paper analyzes the Unruh effect in Lorentz-violating gravity, specifically in the low-energy limit of Hořava–Lifshitz gravity (khronometric/Einstein-Æther theory). It constructs a boost-invariant Rindler patch with a uniformly accelerated æther that features a universal horizon and computes both the Bogolubov temperature and the response of an Unruh–DeWitt detector.

While the Lorentz-violating matter sector admits a straightforward relativistic limit by taking the dispersion scale to infinity, recovering Lorentz symmetry in the gravitational sector is less direct. The authors note that the æther continues to couple to the detector even when the matter sector becomes relativistic. They argue that, in a suitable low-energy limit, quantum-gravity effects should cease and the detector ought to decouple from the æther, restoring the relativistic causal structure, but they indicate that the concrete mechanism achieving this restoration is not currently known.