Related papers: A rigorous formulation of the cosmological Newtoni…
We establish the existence of a wide class of inhomogeneous relativistic solutions to the Einstein-Euler equations that are well approximated on cosmological scales by solutions of Newtonian gravity. Error estimates measuring the difference…
We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…
We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of the Einstein-Euler equations which…
It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for…
We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…
We describe a wide class of inhomogeneous relativistic solutions that are well approximated on cosmological scales by solutions of Newtonian gravity. Error estimates measuring the difference between the Newtonian and relativistic solutions…
We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter $\ep=v_T/c$ $(0<\ep < \ep_0)$, where $c$ is the speed of light, and $v_T$ is a typical…
We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations for which the fluid density and spatial three-velocity converge to a solution of the Poisson-Euler equations of Newtonian gravity. The results…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…
In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results.
Exact solutions of the Einstein's field equations describing a spherically symmetric cosmological model without a big bang or any other kind of singularity recently obtained by Dadhich and Patel (2000) are revisited. The matter content of…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
We derive the `exact' Newtonian limit of general relativity with a positive cosmological constant $\Lambda$. We point out that in contrast to the case with $\Lambda = 0 $, the presence of a positive $\Lambda$ in Einsteins's equations…
The holographic principle sets an upper bound on the total entropy content of the Universe. Within the limits of a Newtonian approximation, a quantum-mechanical model is presented to describe the cosmological fluid. Under the assumption…
The cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…
We have found exact constant solutions for the cosmological density parameter using a generalization of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum and the Newtonian gravitation constant.…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to…