Efficient Computation of Causality in Globally-Hyperbolic Spacetimes Using Link Invariants and its Applications to Plasma Electrodynamics

Causality is a property which compares the speed at which particles can travel between two points in a spacetime to the speed of light. More efficient causality detection has many applications to plasma electrodynamics, specifically, in deriving the Landau damping of plasma waves using the Kramers-Kronig relations, whose derivation depends heavily on causality. With this fundamental connection between causality and the damping of plasma waves, improvements in detection algorithms have further applications to specifying time direction in general plasma physics. Due to its significance, attempts have been made to detect causality, but were inefficient. In this project, we design a more efficient causality detection algorithm for a class of spacetimes known as globally-hyperbolic spacetimes using link invariants. We use the Low Conjecture to represent relationships between points in spacetime using link diagrams. Results from cocycle invariant calculations showed a clear distinction between causal and non-causal links; further use of a queue and constant term reduction enhanced efficiency. Combining this differentiation with data from the Alexander Conway Invariant yielded a detection algorithm which is competitive to those in the literature and sometimes even outperforming them.