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This is the first in a series of papers in which the gradient flows of fundamental curvature invariants are used to formulate a visualization of curvature. We start with the construction of strict Newtonian analogues (not limits) of…
We construct the simplest solution of the Einstein equations that incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric whose equation of state accounts for the Hubble constant and the microwave background radiation…
In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular correspondence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is…
We examine the effect on cosmological evolution of adding a Gauss-Bonnet term to the standard Einstein-Hilbert action for a (1 + 3)+ d dimensional Friedman-Robertson-Walker (FRW) metric. By assuming that the additional dimensions compactify…
In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
The Einstein-Cartan equations in first-order action of torsion are considered. From Belinfante-Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
Recent developments in observational cosmology have led to attempts to make modifications on both sides of the Einstein equation to explain some of the puzzling new findings. What follows is an examination of the source of gravity that we…
We modify the Einstein-Schrodinger theory to include a cosmological constant $\Lambda_z$ which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant $\Lambda_z$ is…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
Based on the Newtonian mechanics, in this article, we present a heuristic derivation of the Friedmann equations, providing an intuitive foundation for these fundamental relations in cosmology. Additionally, using the first law of…
Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black…
We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with…
We show that the $f(R)$-gravity theories with constant Ricci scalar in the Jordan/Einstein frame can be described by Einstein or Einstein-Maxwell gravity with a cosmological term and a modified gravitational constant. We also propose a…
The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…
Modern cosmological theory is based on the Friedmann--Robertson--Walker (FRW) metric. Often written in terms of co-moving coordinates, this well-known solution to Einstein's equations owes its elegant and highly practical formulation to the…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
In this paper we present a number of examples of exact solutions for the Friedmann cosmological equation for metric $ F(R) $ gravity model. Emphasis was placed on the possibility of obtaining exact time dependences of the main cosmological…