Related papers: Comment on "The complete Schwarzschild interior an…
An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular}…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
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…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
We apply the Darmois and the $C^3$ matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
In this article, we prove the local well-posedness of the free-boundary Lin-Liu equations describing the motion of inviscid nematic liquid crystals in the presence of surface tension in Lagrangian coordinates. It is well known that a priori…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
In Paper I in this series we constructed evolution equations for the complete gauge-invariant linear perturbations of a time-dependent spherically symmetric perfect fluid spacetime. A key application of this formalism is the interior of a…
In Ref. [1], exact (not only conformally related) analogue models for the Schwarzschild and Reissner-Nordstr\"om spacetimes were found. The background non-relativistic fluid flow was sustained by an external body force which is not affected…
The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of…
Utilizing the ADM equations, we derive a metric and reduced field equations describing a general, spherically symmetric perfect fluid. The metric describes both the interior perfect fluid region and exterior vacuum Schwarzschild spacetime…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
The analytical structure of the difference between the static vacuum solution in the nonsymmetric gravitational theory (NGT) and the Schwarzschild solution of Einstein's gravitational theory (EGT) is studied. It is proved that a smooth…
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation, the…
Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change…