Axially symmetric static sources of gravitational field

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.

17 pages, 13 figures and 3 tables, typos corrected, published in CQG: Class. Quantum Grav. 33, 235005, (2016)

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• Constraining the equation of state of supra-nuclear dense matter from XMM-Newton observations of neutron stars in globular clusters
• Explicit multipole moments of stationary axisymmetric spacetimes
• Calculation of, and bounds for, the multipole moments of stationary spacetimes
• Generating static perfect-fluid solutions of Einstein's equations

Cited by in corpus (12)

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• Non-spherical sources of Schwarzschild space-time
• Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
• A new class of anisotropic rotating fluids and some throat-like sources for Kerr metric as examples
• An algorithm to generate anisotropic rotating fluids with vanishing viscosity
• Whom actually do multipole moments belong to?
• Physically viable rotating mass solutions surrounding Kerr black hole
• Luminosity of accretion disks in compact objects with quadrupole