Title: The mass-angular momentum inequality for asymptotically flat and asymptotically hyperbolic initial data
Speaker: Marcus Khuri, SUNY Stony Brook
Seminar Type: PDE
Abstract: Consider axisymmetric initial data for the Einstein equations, having two ends, one asymptotically flat or asymptotically hyperbolic and the other either asymptotically flat or asymptotically cylindrical. Heuristic physical arguments lead to the following inequality \(m\geq\sqrt{|J|}\) relating the total mass and angular momentum. Equality should be achieved if and only if the data arise from the exrteme Kerr spacetime. When the designated end is asymptotically flat, Dain established this inequality (along with the corresponding rigidity statement) when the data are maximal and vacuum, and subsequently several authors have improved upon and extended these results. Here we consider the general non-maximal case in which the matter fields satisfy the dominant energy condition, and introduce a natural deformation back to the maximal case which preserves all the relevant geometry. This procedure may then be used to establish the angular momentum-mass inequality (and rigidity statement) in the general case, assuming that a solution exists to a canonical system of two elliptic equations. This is joint work with Ye Sle Cha. When the designated end is asymptotically hyperbolic (modeling asymptotically null slices in asymptotically Minkowski spacetimes), similar results hold. This is joint work with Anna Sakovich.
