Gravitational field of compact objects in general relativity

Abstract

We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that none of the standard models obtained by using Fock's method can be used as an interior source for the approximate exterior Kerr solution. We then use Fock's method to derive a generalized interior solution, and also an exterior solution that turns out to be equivalent to the exterior Hartle-Thorne approximate solution that, in turn, is equivalent to an approximate limiting case of the exact Quevedo-Mashhoon solution. As a result we obtain an analytic approximate solution that describes the interior and exterior gravitational field of a slowly rotating and slightly deformed astrophysical object.

15 pages, published in Phys. Rev. D.: http://prd.aps.org/pdf/PRD/v86/i6/e064043

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Cited by in corpus (16)

• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• Fast Rotating Neutron Stars with Realistic Nuclear Matter Equation of State
• On the induced gravitational collapse scenario of gamma-ray bursts associated with supernovae
• Uniformly rotating neutron stars in the global and local charge neutrality cases
• Quasinormal Modes of a Black Hole with Quadrupole Moment
• Structure-preserving numerical simulations of test particle dynamics around slowly rotating neutron stars within Hartle-Thorne approach
• On Relativistic Multipole Moments of Stationary Spacetimes
• Neutrino oscillation in the $q$-metric
• Fluid sphere: stability problem and dimensional constraint
• Geodesics in the field of a rotating deformed gravitational source
• On the equivalence of approximate stationary axially symmetric solutions of Einstein field equations
• Ernst formulation of axisymmetric fields in $f(R)$ gravity: applications to neutron stars and gravitational waves
• Source integrals of multipole moments for static space-times
• Penrose process in magnetized non-Kerr rotating spacetime with anomalous quadrupole moment
• Approximate Metric for a Rotating Deformed Mass
• Perturbation of the Kerr Metric