# Existence of families of spacetimes with a Newtonian limit

@article{Oliynyk2009ExistenceOF,
title={Existence of families of spacetimes with a Newtonian limit},
author={Todd A. Oliynyk and Bernd Schmidt},
journal={General Relativity and Gravitation},
year={2009},
volume={41},
pages={2093-2111}
}
• Published 20 June 2009
• Physics
• General Relativity and Gravitation

### On Newton-Cartan Cosmology ∗

• Physics
• 1996
Abstract. After a brief summary of the Newton-Cartan theory in a form which emphasizes its close analogy togeneral relativity, we illustrate the theory with selective applications in cosmology. The

### On the existence of rotating stars in general relativity

AbstractThe Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit $$\lambda = \frac{1}{{c^2 }} \to 0$$ of Einstein's equations. For a sufficiently small constant

### Post-Newtonian Expansions for Perfect Fluids

We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations that have a first post-Newtonian expansion. The results here are based on the elliptic-hyperbolic

### The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system

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

### On Newton-Cartan Cosmology

After a brief summary of the Newton-Cartan theory in a form which emphasizes its close analogy to general relativity, we illustrate the theory with selective applications in cosmology. The

### Examples of Newtonian limits of relativistic spacetimes

A frame theory encompassing general relativity and Newton - Cartan theory is reviewed. With its help, a definition is given for a one-parameter family of general relativistic spacetimes to have a

### Covariant Newtonian limit of Lorentz space-times

The formulation of this limit given by Dautcourt [1] is slightly improved using the notions of Galilei manifold and Newtonian connection. It is then shown under what conditions the conservation

### Galilei and Lorentz structures on space-time : comparison of the corresponding geometry and physics

A Galilei (Lorentz) structure on a manifold V is defined as a reduction of the bundle of linear frames to a subbundle of frames invariant under the homogeneous Galilei (Lorentz) group. Galileian or