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.

arXiv comment17 pages, 13 figures and 3 tables, typos corrected, published in CQG: Class. Quantum Grav. 33, 235005, (2016)

References in corpus (17)

• The Equation of State from Observed Masses and Radii of Neutron Stars
• The maximum mass and radius of neutron stars and the nuclear symmetry energy
• The Mass and Radius of the Neutron Star in 4U 1820-30
• Quadrupole moments of rotating neutron stars
• Quadrupole moments of rotating neutron stars and strange stars
• Constraining the equation of state of supra-nuclear dense matter from XMM-Newton observations of neutron stars in globular clusters
• Microscopic calculation of the equation of state of nuclear matter and neutron star structure
• Axially symmetric static sources: A general framework and some analytical solutions
• Non-spherical sources of static gravitational fields: investigating the boundaries of the no-hair theorem
• Explicit multipole moments of stationary axisymmetric spacetimes
• Static axisymmetric space-times with prescribed multipole moments
• Geodesics in a quasispherical spacetime: A case of gravitational repulsion
• Measuring multipole moments of Weyl metrics by means of gyroscopes
• Calculation of, and bounds for, the multipole moments of stationary spacetimes
• A source of a quasi--spherical space--time: The case for the M--Q solution
• Generating static perfect-fluid solutions of Einstein's equations
• The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy

Cited by in corpus (17)

• Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects
• Complexity factors for axially symmetric static sources
• A family of charged compact objects with anisotropic pressure
• Effects of gravitational lensing on neutrino oscillation in $\gamma$-spacetime
• Interior solution for the Kerr metric
• On magnetized anisotropic stars
• Approximate perfect fluid solutions with quadrupole moment
• Self-similarity in static axially symmetric relativistic fluids
• Axially symmetric ghost stars
• A new class of anisotropic rotating fluids and some throat-like sources for Kerr metric as examples
• Non-spherical sources of Schwarzschild space-time
• Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
• An algorithm to generate anisotropic rotating fluids with vanishing viscosity
• Whom actually do multipole moments belong to?
• On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
• Physically viable rotating mass solutions surrounding Kerr black hole
• Luminosity of accretion disks in compact objects with quadrupole