k-Essence, superluminal propagation, causality and emergent geometry

TL;DR

The paper analyzes k-essence theories where perturbations can propagate faster than light on nontrivial backgrounds. By deriving the emergent acoustic metric $G^{\mu\nu}$ and its relation to the background metric, it shows that causality is governed by stable, background-dependent cones and that the standard gravitational metric $g_{\mu\nu}$ remains a universal boundary for propagation of localized configurations. Using Wald's stable causality framework, the authors argue that no closed causal curves arise in cosmological and black-hole accretion contexts, though some exotic backgrounds could in principle admit CCCs; chronology protection via quantum effects is proposed as a safeguard. They also clarify how to pose well-defined Cauchy problems, both on conventional hypersurfaces and in fast-moving frames, and discuss the extent to which the gravitational metric remains universal. Overall, superluminal k-essence signals are shown to be causally safe and conceptually illuminated by the emergent-geometry viewpoint, with implications for analogue gravity and cosmology.

Abstract

The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.