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dc.contributor.authorAkbar, Mohammaden_US
dc.description.abstractIt is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painleve-Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painleve-Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.en_US
dc.publisherElsevier B.V.en_US
dc.rightsCC BY 4.0 (Attribution)en_US
dc.rights©2017 The Authoren_US
dc.sourcePhysics Letters B
dc.subjectSpace and timeen_US
dc.subjectFoliations (Mathematics)en_US
dc.subjectRicci flowen_US
dc.titleSpherical Spacelike Geometries in Static Spherically Symmetric Spacetimes: Generalized Painleve-Gullstrand Coordinates, Foliation, and Embeddingen_US
dc.description.departmentSchool of Natural Sciences and Mathematicsen_US
dc.identifier.bibliographicCitationAkbar, M. M.. 2017. "Spherical spacelike geometries in static spherically symmetric spacetimes: Generalized Painleve-Gullstrand coordinates, foliation, and embedding." Physics Letters B 769: 372-376.en_US
dc.contributor.utdAuthorAkbar, Mohammaden_US
dc.contributor.Scopus56212773400 (Akbar, M)en_US

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Except where otherwise noted, this item's license is described as CC BY 4.0 (Attribution)