Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Newtonian Limits of Isolated Cosmological Systems on Long Time Scales Ann. Henri Poincar´ e 19 (2018), 2157–2243 2018 Springer International Publishing AG, part of Springer Nature 1424-0637/18/072157-87 published online June 4, 2018 Annales Henri Poincar´ e https://doi.org/10.1007/s00023-018-0686-2 Newtonian Limits of Isolated Cosmological Systems on Long Time Scales Chao Liu and Todd A. Oliynyk Abstract. We establish the existence of 1-parameter families of -dependent solutions to the Einstein–Euler equations with a positive cosmological constant Λ > 0 and a linear equation of state p =  Kρ,0 <K ≤ 1/3, for the parameter values 0 << . These solutions exist globally to the future, converge as   0 to solutions of the cosmological Poisson– Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions. 1. Introduction Gravitating relativistic perfect fluids are governed by the Einstein–Euler equa- tions. The dimensionless version of these equations with a cosmological con- stant Λ is given by μν μν μν ˜ ˜ G +Λg˜ = T , (1.1) μν ˜ ˜ ∇ T =0, (1.2) μν where G is the Einstein tensor of the metric μ ν g ˜ =˜ g d¯ x d¯ x , μν and μν μ ν μν T =(ρ¯+¯ p)˜ v v ˜ +¯ pg http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-018-0686-2
Publisher site
See Article on Publisher Site

Abstract

Ann. Henri Poincar´ e 19 (2018), 2157–2243 2018 Springer International Publishing AG, part of Springer Nature 1424-0637/18/072157-87 published online June 4, 2018 Annales Henri Poincar´ e https://doi.org/10.1007/s00023-018-0686-2 Newtonian Limits of Isolated Cosmological Systems on Long Time Scales Chao Liu and Todd A. Oliynyk Abstract. We establish the existence of 1-parameter families of -dependent solutions to the Einstein–Euler equations with a positive cosmological constant Λ > 0 and a linear equation of state p =  Kρ,0 <K ≤ 1/3, for the parameter values 0 << . These solutions exist globally to the future, converge as   0 to solutions of the cosmological Poisson– Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions. 1. Introduction Gravitating relativistic perfect fluids are governed by the Einstein–Euler equa- tions. The dimensionless version of these equations with a cosmological con- stant Λ is given by μν μν μν ˜ ˜ G +Λg˜ = T , (1.1) μν ˜ ˜ ∇ T =0, (1.2) μν where G is the Einstein tensor of the metric μ ν g ˜ =˜ g d¯ x d¯ x , μν and μν μ ν μν T =(ρ¯+¯ p)˜ v v ˜ +¯ pg

Journal

Annales Henri PoincaréSpringer Journals

Published: Jun 4, 2018

References

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