Abstract
We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Hořava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable causal hierarchies can indeed be established, and discuss the implications for the interplay between “superluminal” propagation and causality. The key distinguishing feature is whether the signal velocity is finite or infinite. Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity.
Highlights
Informs the sometimes contentious discussions concerning the interplay between possible superluminal propagation and causality
Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity
We shall seek to generalize the causal hierarchy beyond standard general relativity, to various modified theories of gravity, including multi-metric models, Einstein-aether models, Hořava-like models, modified dispersion relations, etcetera
Summary
The standard general relativistic causal hierarchy is pedagogically outlined in many places. Closed non-spacelike curves with a timelike segment lead to violation of the chronology condition. We may want to rule out those spacetimes that are arbitrary close to violating the hierarchy of causality conditions above To this end, we construct a partial ordering on the space of Lorentzian metrics L(M ) by saying that one metric [g]ab is “wider” than another second metric [g]ab, denoted [g]ab > [g]ab, if all non-spacelike vectors in the second metric are strictly timelike in the first metric. For the discussion it will be important to keep in mind that, being a partial order, not every pair of metrics need to be comparable With this in mind, the step in the hierarchy, the stable causality condition, can be defined in at least 3 equivalent ways:. We shall seek to extend this framework beyond standard general relativity
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
