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Numerically estimating the Weyl tensor for a causal set sprinkled in a plane gravitational wave

Mathematical Physics Seminar

Speaker: Nauman Ibrahim, Ole Miss
Related Webpage: TBA
Location: 3024 PDSB
Start time: Mon, Jun 2 2025, 4:15PM

A significant effort in causal set theory (CST), a theory about the deep structure of spacetime purporting that that the continuum gives way to a set of elements with a causal order between them, is the construction of discrete analogs of continuum geometrical quantities. We propose an idea for numerically estimating the Weyl tensor for a causal set representing a plane gravitational wave (a sprinkling into such a spacetime) by extracting (constructing) the analog of geodesic deviation in a causal set. Consequently, we present some of the necessary ingredients that must go into this construction, namely: a method for finding the causal relations between sprinkled points, a fast algorithm for finding the discrete analogs of timelike geodesics between two points, the longest chains between them (which can be thought of as a "tube" around the continuum geodesic), and a statistical characterization of the width and shape of these "tubes".



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