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Explore a specialized lecture on general relativity formulation using generalized harmonic gauge on compactified hyperboloidal slices with a novel 2+1+1 decomposition approach. Learn how evolved fields and equations of motion depend on the choice of outgoing and ingoing null vectors, and discover how all geometric quantities decompose against these vectors. Examine spherically-symmetric numerical evolution results that successfully recover expected physics at null infinity, where decay behavior naturally follows the 'good-bad-ugly' classification system with regularization achieved through carefully selected gauge source functions. Gain insights into the mathematical framework that enables this approach and understand the ongoing research extending these methods to three-dimensional cases, providing a comprehensive view of advanced techniques in numerical relativity and hyperboloidal foliations.
