Related papers: A perfect-fluid spacetime for a slightly deformed …
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
Some years ago, a new powerful technique, known as the Classical Effective Field Theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically…
We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent…
We examine charged static perfect fluid distributions with a dilaton field in the frame-work of general relativity. We consider the case that the Einstein equations reduce to a non-linear version of Poisson equation. We show that Maxwell…
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…
Analyzing the spacetime for a static spherically distributed perfect fluid we show that the smooth matching of the interior and exterior metrics for a realistic source is possible only for the distances from the origin that exceeds the…
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and…
Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
The Einstein field equation as an equation of state of a thermodynamical system of spacetime is reconsidered in the present Letter. We argue that a consistent interpretation leads us to identify scalar curvature and cosmological constant…
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the…
A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary,…