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A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
We discuss the relationship between Schlesinger system and stationary axisymmetric Einstein's equation on the level of algebro-geometric solutions. In particular, we calculate all metric coefficients corresponding to solutions of Ernst…
We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
Eigenfunctions are shown to constitute privileged coordinates of self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. The formalism developed here may be used to link…
We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically…
Extending the approach developed by Ara\'ujo and Stoeger [1] and improved in Ara\'ujo {\it et al} [2], we have shown how to construct dust-filled $\Lambda \neq 0$ Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmological models from FLRW…
We formulate Friedmann's equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the $\beta$-times $t_\beta:=\int^t a^{-2\beta}$, where $a$ is the scale…
Einstein gravity at $D\rightarrow 2$ limit can be obtained from the Kaluza-Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar-tensor theory can be further…
A generalized model of space-time is given, taking into consideration the anisotropic structure of fields which are depended on the position and the direction (velocity).In this framework a generalized FRW-metric the Raychaudhouri and…
We investigated the back reaction of cosmological perturbations on the evolution of the universe using the second order perturbation of the Einstein's equation. To incorporate the back reaction effect due to the inhomogeneity into the…
Torsion arising from fermionic matter in the Einstein-Cartan formulation of general relativity is considered in the context of Robertson-Walker geometries and the early Universe. An ambiguity in the way torsion arising from hot fermionic…
When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann…
We study the modified Friedmann equation in the Friedmann-Robertson-Walker universe with quantum effect. Our modified results mainly stem from the new entropy-area relation and the novel idea of T. Padmanabhan, who considers the cosmic…
In this paper we apply dimensional analysis (D.A.) to two cosmological models: Einstein-de Sitter and one Friedmann-Robertson-Walker (FRW) with radiation predominance. We believe that this method leads to the simplest form of solution the…
We investigate torsion-driven cosmological dynamics within the framework of Einstein-Cartan gravity using the De Donder-Weyl Hamiltonian formalism, where the tetrad and Lorentz connection act as independent variables and the Hamiltonian…
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual…
As an extension of the Robinson-Trautman solutions of D=4 general relativity, we investigate higher dimensional spacetimes which admit a hypersurface orthogonal, non-shearing and expanding geodesic null congruence. Einstein's field…