Spacelike manifolds with bounded Hawking mass
Time and place
1 PM on Monday, April 7th, 2014; NAC 1/511E
Dr. Christina Sormani (Lehman College and CUNY GC)
Abstract
We consider sequences of three dimensional rotationally symmetric and time symmetric spacelike surfaces with boundary, $M_j$, that have nonnegative scalar curvature and uniformly bounded Hawking mass, depth and boundary area. Such spacelike surfaces arise naturally in General Relativity in the vicinity of a single star, planet, spherical dust cloud or black hole. The Hawking mass is determined completely by the mean curvature and area of the boundary of the region. If such a region has 0 Hawking mass, then the region contains no particles of any mass and in fact the region is a Euclidean disk [Hawking]. In prior work with Dan Lee (Queens College), we proved that if the sequence has Hawking mass converging to 0 then the sequence converges in the intrinsic flat sense to a Euclidean disk. In recent work with Philippe LeFloch (Universitè Pierre et Marie Curie) we provide a precise estimate on the intrinsic flat distance to a disk depending upon the Hawking mass, depth and boundary area. We also prove that when a sequence, $M_j$ has only $H^1$ regularity, then a subsequence must converge in the intrinsic flat sense within the same class of spaces. In this setting, we show the area of the boundary and the Hawking mass are both continuous under the intrinsic flat convergence. Note that ordinarily intrinsic flat limits are only rectifiable (not $H^1$) and the area is usually only semicontinuous under intrinsic flat convergence. More information on intrinsic flat convergence, which was first defined in joint work with Stefan Wenger (University of Fribourg), may be found at http://comet.lehman.cuny.edu/sormani/intrinsicflat.html
