Related papers: Time-dependent Spherically-symmetric 5-D Vacuum So…
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…
Spherically symmetric static vacuum solutions have been built in $f(T)$ models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with…
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…
In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
We solve the five dimensional vacuum Einstein equations for several kinds of anisotropic geometries. We consider metrics in which the spatial slices are characterized as Bianchi types-II and V, and the scale factors are dependent both on…
We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the…
We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action arising from trace dynamics. We give analytic and numerical results for the…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
We consider a general non-linear sigma model coupled to Einstein gravity and show that in spherical symmetry and for a simple realization of self-similarity, the spacetime can be completely determined. We also examine some more specific…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
Exact solutions of the Einstein's field equations describing a spherically symmetric cosmological model without a big bang or any other kind of singularity recently obtained by Dadhich and Patel (2000) are revisited. The matter content of…