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Explore a 25-minute physics lecture that delves into the mapping of geodesics from 4D spacetime to lower-dimensional manifolds through effective metrics. Learn how spacetimes with two Killing vector fields can be simplified while maintaining their essential physical properties, with particular focus on null and timelike circular orbits. Discover the analytical framework used to study circular orbits around black holes and exotic compact objects, gaining valuable insights into orbital stability and dynamics in strong gravitational fields. Presented at the Workshop on "Lensing and Wave Optics in Strong Gravity" at the Erwin Schrödinger International Institute for Mathematics and Physics, this talk demonstrates how dimensional reduction techniques can serve as powerful tools for both analytical and numerical studies of complex spacetime geometries.
