Math @ Duke

Publications [#354060] of Demetre P Kazaras
Papers Accepted
 Sven Hirsch, Demetre Kazaras, Marcus Khuri, Spacetime Harmonic Functions and the Mass of 3Dimensional Asymptotically Flat Initial Data for the Einstein Equations,
Journal of Differential Geometry
(2020)
(last updated on 2020/12/18)
Abstract: We give a lower bound for the Lorentz length of the ADM energymomentum vector (ADM mass) of 3dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic functions' in addition to the energymomentum density of matter fields, and is valid regardless of whether the dominant energy condition holds or whether the data possess a boundary. A corollary of this result is a new proof of the spacetime positive mass theorem for complete initial data or those with weakly trapped surface boundary, and includes the rigidity statement which asserts that the mass vanishes if and only if the data arise from Minkowski space. The proof has some analogy with both the Witten spinorial approach as well as the marginally outer trapped surface (MOTS) method of Eichmair, Huang, Lee, and Schoen. Furthermore, this paper generalizes the harmonic level set technique used in the Riemannian case by Bray, Stern, and the second and third authors, albeit with a different class of level sets. Thus, even in the timesymmetric (Riemannian) case a new inequality is achieved.


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