The shear-free condition and constant-mean-curvature hyperboloidal initial data. (3rd May 2016)

• Record Type: Journal Article
• Authors: Allen, Paul T; Isenberg, James; Lee, John M; Allen, Iva Stavrov
• Is Part Of: Classical and quantum gravity. Volume 33:Number 11(2016:Jun.)
• Publication Date: 2016-05-03
• Subjects: Einstein constraint equations -- asymptotically hyperboloidal -- shear-free -- general relativity; Primary 35Q75 -- Secondary 53C80 -- 83C05; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/11/115015
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: We consider the Einstein–Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conformal boundary at future null infinity; see (Andersson and Chruściel 1994 Commun. Math. Phys. 161 533–68 ). We work with initial data sets in a variety of regularity classes, primarily considering those data sets whose geometries are weakly asymptotically hyperbolic, as defined in (Allen et al 2015 arXiv:1506.03399 ). These metrics are C 1, 1 conformally compact, but not necessarily C 2 conformally compact. In order to ensure that the data sets we construct are indeed shear-free, we make use of the conformally covariant traceless Hessian introduced in (Allen et al 2015 arXiv:1506.03399 ). We furthermore construct a class of initial data sets with weakly asymptotically hyerbolic metrics that may be only C 0, 1 conformally compact; these data sets are insufficiently regular to make sense of the shear-free condition.