Noncommutative Geometry Seminar

Date: November 9, 2022

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Dan Lee, Queens College CUNY

Title: The equality case of the spacetime positive mass theorem

Abstract: The spacetime positive mass theorem states that asymptotically flat initial data sets satisfying the dominant energy condition (a physical condition expressing nonnegativity of matter sources) must have “nonnegative mass” in the sense that the ADM energy-momentum vector (E,P) must be “future causal,” that is, E \ge |P|. This result goes back to Witten in the spin case and Schoen-Yau and Eichmair-Huang-Lee-Schoen for manifolds with dimension less than 8. It was always conjectured that the equality E=|P| should only be possible for initial data sets arising from slices of Minkowski space, but it is surprisingly tricky to prove. A rigorous proof in the spin case was not discovered until 15 years after Witten’s proof, by Beig-Chrusciel (n=3) and Chrusciel-Maerten (n>3). Recently, in joint work with Lan-Hsuan Huang, we built on some insights of Beig-Chrusciel to find a proof that depends only upon knowing that the inequality E \ge |P| holds for all nearby initial data sets that also satisfy the hypotheses of the spacetime positive mass theorem. Or in other words, our proof characterizing the equality case does not depend on *how* one proves the inequality.