Related papers: A Kerr interior
The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein's…
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution,…
A stationary axially symmetric solution describing a rotating anisotropic source for Einstein Field Equations(EFE) is proposed which matches to the exterior Kerr metric. The anisotropic source satisfies all energy conditions - weak, strong,…
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
The Einstein field equations have no known and acceptable interior solution that can be matched to an exterior Kerr field. In particular, there are no interior solutions that could represent objects like the Earth or other rigidly rotating…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
A central problem in General Relativity is obtaining a solution to describe the source's interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of…
We present a novel approach for the construction of interior solutions for the Kerr metric, extending J. Ovalle's foundational work through ellipsoidal coordinate transformations. By deriving a physically plausible interior solution that…
Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the…
In an important series of articles published during the 70's, Krasi\'nski displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of perfect fluid. However, these…
Rotating black holes are algebraically special solutions to the vacuum Einstein equation. Using properties of the algebraically special solutions we construct the dual fluid, which flows on black hole horizon. An explicit form of the Kerr…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these…
While non-rotating black-hole solutions are well known in Einstein--\ae{}ther gravity, no axisymmetric solutions endowed with Killing horizons have been so far found outside of the slowly rotating limit. Here we show that the Kerr spacetime…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…