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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…
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…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…
We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.
Requiring all massless elementary fields to have conformal scaling symmetry removes a conflict between gravitational theory and the quantum theory of elementary particles and fields. Extending this postulate to the scalar field of the Higgs…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become…
In cosmology based on general relativity, the universe is modeled as a fluid. The transition from the Einstein field equation to its large-scale (cosmological) version is thus analogous to the transition, for a system consisting of a large…
The thermodynamic interpretation of the Stephani Universes is studied in detail. The general expression of the speed of sound and of the thermodynamic schemes associated with a thermodynamic solution is obtained. The constraints imposed on…
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
The Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field are shown to be described in a unified way, formally identical to the dynamics of a relativistic…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
Neutrinos interacting with the quintessence field can trigger the accelerated expansion of the Universe. In such models with a growing neutrino mass the homogeneous cosmological solution is often unstable to perturbations. We present…
We examine the consequences of a universe with a non-constant cosmological term in Einstein's equations and find that the Bianchi identities reduce to the first law of thermodynamics when cosmological term is identified as being…
The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based…
We use the formalism of Geometrothermodynamics to derive a series of fundamental equations for thermodynamic systems. It is shown that all these fundamental equations can be used in the context of relativistic cosmology to derive diverse…
By using the thermodynamic theory of irreversible processes and Einstein general relativity, a cosmological model is proposed where the early universe is considered as a mixture of a scalar field with a matter field. The scalar field refers…
We study the back reaction effect of massless minimally coupled scalar field at finite temperatures in the background of Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the…