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{\it If gravity is a metric field by Einstein, it is a Higgs field.} Gravitation theory meets spontaneous symmetry breaking in accordance with the Equivalence Principle reformulated in the spirit of Klein-Chern geometries of invariants. In…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
In this paper, we give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use scaling stable solitons for nonlinear wave equations to approximate the test particle. Given a vacuum spacetime $([0,…
The unification of the Einstein theory of gravity with a conformal invariant version of the standard model for electroweak interaction without the Higgs potential is considered. In this theory, a module of the Higgs field is absorbed by the…
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
General relativity can be cast as a gauge theory by introducing a tetrad field and a spin-connection. This formalism was extended by replacing the tetrad field with a mixed tensor field independent of the metric tensor in order to develop a…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from…
General relativity is a non-linear theory with the distinguishing feature that gravitational field energy also acts as gravitational charge density. In the well-known Schwarzschild solution describing field of an isolated massive body at…
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
The main objective of this paper is to investigate the $m$-quasi Einstein manifold when the potential function becomes convex. In this article, it is proved that an $m$-quasi Einstein manifold satisfying some integral conditions with…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where…
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\`e}re boundary conditions gr-qc/0610130. These…
We study the gravitational collapse of a non-interacting mix of perfect fluid and a spatially homogeneous scalar field within a Chiellini-integrable framework. We choose an extended Higgs-type self-interaction potential and reduce the…
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between…
We consider extra compact dimensions as the origin of a cosmological universal energy density in the regular dimensions, with only graviton fields propagating in the compact space dimensions. The quantum zero point energy originating from…