Vindula Kumaranayake : Rigidity Theorems in General Relativity

Rigidity theorems show that, under symmetry or asymptotic assumptions, solutions to the Einstein vacuum equations collapse to a handful of distinguished metrics. This talk gives modern, self-contained proofs of four classical results: Birkhoff's theorem, Lichnerowicz's theorem, Robinson's generalisation of Israel's uniqueness theorem, and the Boucher–Gibbons–Horowitz rigidity theorem for anti-de Sitter spacetime, and highlights a unifying template underlying the last two: constructing a divergence identity, integrating it between carefully chosen hypersurfaces, and using positivity to force curvature obstructions to vanish.