Related papers: An Embedding for General Relativity and its Implic…
Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
We consider the background cosmological solutions in the $6D$ (six-dimensional) model with one time and five space coordinates. The theory of our interest has the action composed by the Einstein term, cosmological constant, and two…
We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza-Klein theory (or 10D superstrings and 11D supergravity). We argue that…
We find new solutions to the five-dimensional Einstein-Maxwell-dilaton theory with cosmological constant where the dilaton field couples to the electromagnetic field as well as to the cosmological term with two different coupling constants.…
We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple…
A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent,…
Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have…
A solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects, and may also provide a description of our universe on length scales…
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These latter solutions are referred to as gravitational solitons.…
We summarize recent results on $D$-dimensional Robinson-Trautman solutions of Einstein's gravity in the presence of a conformally invariant non-linear electromagnetic field and a cosmological constant. These spacetimes contain static dyonic…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
Einstein-Maxwell equations with a cosmological constant are analyzed in a four dimensional stationary spacetime admitting in addition a two dimensional group $G_2$ of spatial isometries. Charged rotating open and closed black string…
It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+\alpha GB_{ab}+\delta^{55}_{ab}\alpha\exp(-2\chi/\sqrt{\alpha})GB_4=0$ and the…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…