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Todd A. Oliynyk 《Communications in Mathematical Physics》2010,295(2):431-463
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 e = vT/c{\epsilon=v_T/c}
(0 < e < e0){(0< \epsilon < \epsilon_0)}, where c is the speed of light, and v
T
is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab
M @ [0,T)×\mathbb T3{M\cong [0,T)\times \mathbb {T}^3}, and converge as
e\searrow 0{\epsilon \searrow 0} to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions
can be expanded in the parameter e{\epsilon} to any specified order with expansion coefficients that satisfy e{\epsilon}-independent (nonlocal) symmetric hyperbolic equations. 相似文献
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Jürgen Ehlers developed frame theory to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter
λ, which can be thought of as 1/c
2, where c is the speed of light. By construction, frame theory is equivalent to general relativity for λ > 0, and reduces to Newtonian gravity for λ = 0. Moreover, by setting , frame theory provides a framework to study the Newtonian limit . A number of ideas relating to frame theory that were introduced by Jürgen have subsequently found important applications
to the rigorous study of both the Newtonian limit and post-Newtonian expansions. In this article, we review frame theory and
discuss, in a non-technical fashion, some of the rigorous results on the Newtonian limit and post-Newtonian expansions that
have followed from Jürgen’s work. 相似文献
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Under study are the ZC-automata and the transformation groups determined by them. We establish relationships between the group
of ZC-automaton transformations and the group of infinite unitriangular integer matrices. We describe the derived series of
the group of ZC-automaton transformations and present conditions for the representability of residually solvable groups by
ZC-automaton transformations. We construct a continual family of ZC-automata with two states, each of which generates a free
semigroup. 相似文献
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La2+xMnGe2+y (I) and Ce2+xMnGe2+y (II) are prepared by arc‐melting of the elements in molar ratios of 2:1:2 followed by annealing (sealed silica tubes, 800 °C, 2 weeks). 相似文献
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We develop some new techniques of constructing (finite state) actions on rooted homogeneous trees and apply them to various groups. In particular we show that there is a faithful action of each amalgameted free product of the form ???? on a rooted homogeneous tree of finite degree, described by finite state automorphisms. 相似文献
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Todd A. Oliynyk 《Communications in Mathematical Physics》2009,288(3):847-886
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 formulation of the Einstein-Euler equations used in [15],
which contains a singular parameter , where v
T
is a characteristic velocity associated with the fluid and c is the speed of light. As in [15], energy estimates on weighted Sobolev spaces are used to analyze the behavior of solutions
to the Einstein-Euler equations in the limit , and to demonstrate the validity of the first post-Newtonian expansion as an approximation. 相似文献