Related papers: An Exact Interior Kerr Solution
An exact solution of the Einstein field equations is proposed which represents a differentially rotating fluid. As this solution matches the exterior Kerr solution and reduces to the Schwarzschild interior solution by setting the rotational…
A generalized analysis of the local entropy production of a simple fluid is used to show that, if intrinsic angular momentum is taken into account, rotational viscosity must arise in the linear non-equilibrium regime. As a consequence, the…
The properties of a star with constant positive energy density inside (as for the Schwarzschild interior geometry) and a negative pressure are investigated, using a static conformally flat spacetime. Because of the negative pressure, the…
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,…
An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the…
We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor $R_\mu^\nu$ and the…
A family of spacetimes suitable for describing the interior of a non-rotational black hole is constructed. The stress-energy tensor is that of a spherically symmetric vacuum, as commonly assumed nowadays. The problem of matching the…
We analyze the stress-energy tensor necessary to generate a general stationary and axisymmetric spacetime. The constraints on the geometry arising from considering a perfect fluid as a source are derived. For a fluid with a nonzero stress…
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…
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…
The line element of a class of solutions which match to the solution of Kerr on an oblate spheroid if the two functions $ F(r)$ and $H(r)$ on which it depends satisfy certain matching conditions is presented. The non vanishing components 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…
Adopting the phantom (ghost) scalar field description of dark energy, we construct a general class of exact interior solutions describing mixed relativistic stars containing both ordinary matter and dark energy in different proportions. The…
A rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally…
In the framework of Einstein's the theory of general relativity we present a new interior solution with a perfect fluid, this is constructed from the proposal of a gravitational redshift factor. The geometry is regular and its density and…
We consider a configuration consisting of a wormhole filled by a perfect fluid. Such a model can be applied to describe stars as well as neutron stars with a nontrivial topology. The presence of a tunnel allows for motion of the fluid,…
An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…
The Kerr metric is a vacuum solution of the Einstein equations outside of a rotating black hole, but what interior matter is actually rotating and sourcing the Kerr geometry? Here, we describe a rotating exotic matter which can source the…
We consider a uniformly luminous radiating sphere and a static black hole located in the center of that sphere. We give analytic formulas for radiation stress-energy tensor components in such a configuration, for the observer located at an…
We derive an exact solution to the Einstein's equations with a stress-energy tensor corresponding to an opposite-sign scalar field, and show that such a solution describes the internal region of a rotating wormhole. We also derive an static…