Related papers: Integrable and non-integrable structures in Einste…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and $f(R,T)$-modifications. The constructions are possible in terms of…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
We report on a new two-parameter class of cosmological solutions to the Einstein-Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.
Dynamic equations that are the simplest conformally invariant generalization of Einstein equations with cosmological term are considered. Dimensions and Weyl weights of the additional geometrical fields (the vector and the antisymmetric…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
Three non-existence results are established for self-gravitating solitons in Einstein-Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function $f(\Phi)$. Firstly, a…
In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory.…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
Einstein field equations with a cosmological constant are approximated to the second order in the perturbation to a flat background metric. The final result is a set of Einstein-Maxwell-Proca equations for gravity in the weak field regime.…
We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations…
We construct a 4-parameter family of inhomogeneous cosmological models, which contains two recently derived 3-parameter families as special cases. The corresponding exact vacuum solution to Einstein's field equations is obtained with…
We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field…
Theories of scalars and gravity, with an Einstein-Hilbert term and non-minimal interactions, $M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange induced contact interactions. These modify the renormalization group, leading to a discrepancy…
The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's…
In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exponential potential forms. The dynamics of Bianchi class A…
All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions $G_4(N)$. The potentials of the admissible electromagnetic fields admit the…
I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are…
Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…