A new class of exact solutions of Einstein’s field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are...

Einstein’s field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits a...

Gauge choice for a spherically symmetric 3-brane embedded in a D-dimensional bulk with arbitrary matter fields on and off the brane is studied. It is shown that Israel’s junction conditions across the brane restrict severely the dependence of the matter fields on the spacetime coordinates. As examples, a scalar field or a Yang-Mills potential can be only either time-dependent or radialcoordinat...

Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid ...

We describe the use of conformalmappings as amathematicalmechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact sta...

Asymptotics of solutions of a perfect fluid when coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry are studied. In particular, it is found that the problem of self-similar solutions of the first kind for a fluid with the equation of state, p = kρ, can be reduced to solving a master equation of the form, 2F (q, k) q(ξ) q(ξ) −G(q, k)q(ξ) = 4 ξ . For k = 0 a...

We present here the general transformation that leaves unchanged the form of the field equations for perfect fluid cosmologies in the DGP braneworld model. Specifically, a prescription for relating exact solutions with different equations of state is provided, and the symmetries found can be used as algorithms for generating new cosmological models from previously known ones. We also present, i...

A simple gravitational model with torsion is studied, and it suggested that could explain the dark matter energy in universe. It can be reinterpreted as a using Einstein equations where spacetime has regions filled perfect fluid negative (pressure) positive mass density, other containing an anisotropic substance rest frame (where momentum zero) density uniaxial stress tensor, possibly “luminal”...

The target of the current research article is to investigate solitonic attributes relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient (GRY-soliton). We exhibit that a filled with density ρ, magnetic field strength H, permeability μ obeys Einstein equation without cosmic constant being generalized quasi-Einstein manifold (GQE). In such sp...

During the previous decade the interest for singularity-free cosmological models was supported by the publication of the first known geodesically complete perfect fluid cosmology [1]. Until then such possibility had been overlooked due to the restrictive conditions imposed by singularity theorems [2], [3]. These theorems required physically reasonable restrictions such as energy, causality and ...