Axially symmetric static sources of gravitational field. (31st October 2016)

• Record Type: Journal Article
• Authors: Hernandez-Pastora, J L; Herrera, L; Martin, J
• Is Part Of: Classical and quantum gravity. Volume 33:Number 23(2016:Dec.)
• Publication Date: 2016-10-31
• Subjects: sources of gravitational field -- multipole moments -- globally regular models; 04.20.Cv -- 04.20.Dw -- 97.60.Lf -- 04.80.Cc; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/23/235005
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match smoothly to some exterior solution of the Weyl family, thereby representing globally regular models describing non-spherical sources of gravitational field. In the spherically symmetric limit, all our models converge to the well known incompressible perfect fluid solution. The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. Some particular sources are obtained, and the physical variables of the energy–momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments. The total mass of different configurations is also calculated, it is shown to be equal to the monopole of the exterior solution.