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Explore cutting-edge challenges in gravitational physics through this comprehensive lecture that examines both theoretical foundations and experimental validations of General Relativity. Begin with a review of high-precision experimental confirmations of Einstein's theory before delving into six major open questions that define current research frontiers. Investigate the intriguing connections between General Relativity and Yang-Mills theory, discovering unexpected mathematical parallels between these fundamental frameworks. Examine the surprising relationships between Einstein's field equations and the Navier-Stokes equations of fluid dynamics, revealing deep structural similarities across different areas of physics. Learn about the emergence of hidden symmetry structures near cosmological singularities and how these mathematical patterns provide insights into the universe's most extreme conditions. Study peeling properties and symmetry structures that manifest near spatial infinity, understanding their implications for gravitational wave theory and asymptotic behavior. Analyze the mathematical technique of skeletonizing black holes as point masses and its applications in computational relativity and gravitational wave detection. Conclude by exploring why viable extensions of General Relativity remain remarkably scarce despite decades of theoretical efforts, examining the constraints that limit modifications to Einstein's framework and the implications for alternative theories of gravity.
