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A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We show the stability of the geometric optics approximation in general relativity by constructing a family $(g_\lambda)_{\lambda\in(0,1]}$ of high-frequency metrics solutions to the Einstein vacuum equations in 3+1 dimensions without any…
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
The basic idea that gravity can be a long-wavelength effect {\it induced} by the peculiar ground state of an underlying quantum field theory leads to consider the implications of spontaneous symmetry breaking through an elementary scalar…
Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…
The geometric properties of General Relativity are reconsidered as a particular nonlinear interaction of fields on a flat background where the perceived geometry and coordinates are "physical" entities that are interpolated by a patchwork…
While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The…
Global topological defects described by real scalar field in (3,1) dimensions coupled to gravity are analyzed. We consider a class of scalar potentials with explicit dependence with distance, evading Derrick's theorem and leading to defects…
Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field…
We discuss the vacuum energy density term resulting from the spontaneous breakdown of the electroweak gauge symmetry, in the Higgs Mechanism. We alternatively expand the scalar field at one of the degenerate states that lie outside the…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
We give a derivation of general relativity and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace with two key properties. The first is…
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new $U_1$ gauge symmetry is repulsive among baryons. Such a…
We study gravitational radiation for a positive value of the cosmological constant $\Lambda$. We rely on two battle-tested procedures: (i) We start from the same null coordinate system used by Bondi and Sachs for $\Lambda = 0$, but,…