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Explore the fundamental role of space-like infinity singularities in general relativity through this 27-minute conference lecture from the Erwin Schrödinger International Institute's Workshop on Hyperboloidal Foliations. Examine how singularities at space-like infinity (i^0) become crucial for characterizing asymptotics in analytical and numerical approaches to non-flat spacetimes. Learn about Friedrich's pioneering Initial Value Problem framework specifically adapted for singularity geometry, where regular asymptotics translate to specific initial data assumptions. Investigate the physically relevant motivations for regulating assumptions, particularly regarding energy-momentum density regularity conditions inspired by the Horowitz and Tod conjecture. Discover the numerical challenges where i^0 is typically excluded through cut-offs or hyperboloidal slicing, and understand the need for unified frameworks to implement consistent initial data across different setups for result comparison. Gain insights into recent developments addressing both analytical and numerical aspects of this complex problem in general relativity.
