4 papers
The spacetime Penrose inequality under a quasi final state hypothesis
Ahmed Ellithy
Penrose's original heuristic for his eponymous spacetime inequality -- a conjectured lower bound on the ADM mass in terms of the area of a horizon cross-section -- relies on the bl…
Local Well-Posedness for the Bartnik Stationary Extension Problem near Schwarzschild Spheres
Ahmed Ellithy
We investigate the Bartnik stationary extension conjecture, which arises from the definition of the spacetime Bartnik mass for a compact region in a general initial data set satisf…
Local Well-posedenss of the Bartnik Static Extension Problem near Schwarzschild spheres
Ahmed Ellithy
We establish the local well-posedness of the Bartnik static metric extension problem for arbitrary Bartnik data that perturb that of any sphere in a Schwarzschild slice.…
Existence of static vacuum extensions for Bartnik boundary data near Schwarzschild spheres
Spyros Alexakis, Zhongshan An, Ahmed Ellithy +1
We obtain existence and local uniqueness of asymptotically flat, static vacuum extensions for Bartnik data on a sphere near the data of a sphere of symmetry in a Schwarzschild mani…