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The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We review the matching conditions for a collapsing anisotropic cylindrical perfect fluid, recently discussed in the literature (2005 {\it Class. Quantum Grav.} {\bf 22} 2407). It is shown that radial pressure vanishes on the surface of the…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base…
In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ represents a stiff or Zeldovich fluid. Using…
We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free and vorticity free solution of Einstein's field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where…
We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius)…
We propose a model for an anisotropic dark energy star where we assume that the radial pressure exerted on the system due to the presence of dark energy is proportional to the isotropic perfect fluid matter density. We discuss various…
Following the scheme developed by Misner and Sharp, we discuss the dynamics of gravitational collapse. For this purpose, an interior cylindrically symmetric spacetime is matched to an exterior charged static cylindrically symmetric…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions.…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
The holostar is an exact spherically symmetric solution to the field equations of general relativity with anisotropic interior pressure. Its properties are similar to a black hole. It has an internal temperature inverse proportional to the…
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear…
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in…
In this work we study the influence of isotropic and anisotropic fluids on the spherically symmetric warp metric. We evaluate the energy conditions and the influence of including a cosmological constant type term. We find that, considering…
We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state $p=\rho/3$ at its center. In the process of the gravitational…
In this paper, we consider the spherically symmetric gravitational collapse of isotropic matter undergoing dissipation in the form of heat flux, with a generalized Vaidya exterior, in the context of $f(R, T)$ gravity. Choosing $f(R,…
In a recent approach in modelling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasised. It is possible to generate a model which is physically reasonable by approximately solving the…