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We study how the changes of coordinates between the class of harmonic coordinates affect the analitycal solutions of Einstein's equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
We prove that in the infinite speed-of-light limit (i.e., non-relativistic and subhorizon limits), the relativistic fully nonlinear cosmological perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
According to maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of total entropy for perfect fluid, which implies that thermodynamic relations contain information of gravity.…
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields.…
In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the…
The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
Spatially homogeneous but totally anisotropic and non-flat Bianchi type II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical…
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
Cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of string fluid as a source of matter. To get the three types of exact solutions of Einstein's field equations we assume $A = f(x)k(t)$, $B =…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two…
In the $\Lambda$CDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The…
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…