Related papers: Initial Data Set For Cosmology: Application to Mat…
With Einstein's inertial motion (free-falling and non-rotating relative to gyroscopes), geodesics for non-relativistic particles can intersect repeatedly, allowing one to compute the space-time curvature $R^{\hat{0} \hat{0}}$ exactly.…
Emergent modified gravity has shown that the canonical formulation of general relativity gives rise to a larger class of covariant modifications than action-based approaches, so far in symmetry-reduced models. This outcome is made possible…
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…
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…
We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
Using the Einstein gravitation theory (EGT) we calculate the Schwarzschild metric that is defined in the surrounding vacuum of a spherically symmetric mass distribution, not in rotation. The field equations of the EGT with this metric were…
An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…
We solve the field equations of modified gravity for $f(R)$ model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase space analysis of $f(R)$ models, both with and without the effects of radiation.…
After the study of non-inertial frames in special relativity with emphasis on the problem of clock synchronization (i.e. of how to define 3-space), an overview is given of Einstein canonical gravity in the York canonical basis and of its…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
We have solved the Einstein-Maxwell equations for a class of isotropic metrics with constant spatial curvature in the presence of magnetic fields. We consider a slight modification of the Tolman averaging relations so that the…
The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse…
In the framework of the concordance cosmological model the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of…
A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…