Stabilizing Relativistic Fluids on Spacetimes with Non-Accelerated Expansion

Fajman, David; Oliynyk, Todd A.; Wyatt, Zoe

doi:10.1007/s00220-020-03924-9

Cited by 31 publications

(27 citation statements)

References 20 publications

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“…While [6] concerns only Newtonian dynamics, it is nevertheless a fair indication that the fully coupled dynamics under the Einstein-fluid system will likely lead to the formation of shocks. Continuing this line of reasoning, we note that although the work [13] also treated linear expansion, the full coupling between gravity and fluid makes our present work highly nontrivial. Indeed the issues highlighted on the previous Section 1.3.1 are indicative of the substantial technical difficulties that arise in the fully coupled EES.…”

Section: λ-Induced Accelerated Expansion and Stabilisation Of Fluidsmentioning

confidence: 53%

“…We consider M = T 3 with a(t c ) = (t c ) p for p > 0. The following table summarises some of the main results concerning linear equation of states p = c 2 S ρ from [32,13], see also [34] c S = 0 Stable [32] In combination, these results indicate that in spacetimes undergoing power-law inflation whether shocks form from small data depends on the equation of state and, in particular in the linear case, on the speed of sound. Indeed the literature suggests that slower speeds of sound reduce the tendency of shock formation.…”

Section: λ-Induced Accelerated Expansion and Stabilisation Of Fluidsmentioning

confidence: 81%

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Slowly expanding stable dust spacetimes

Fajman,

Ofner,

Wyatt

2021

Preprint

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We establish the future nonlinear stability of a large class of FLRW models as solutions to the Einstein-Dust system. We consider the case of a vanishing cosmological constant, which in particular implies that the expansion rate of the respective models is linear i.e. has zero acceleration. The resulting spacetimes are future globally regular. These solutions constitute the first generic class of future regular Einstein-Dust spacetimes not undergoing accelerated expansion and are thereby the slowest expanding generic family of future complete Einstein-Dust spacetimes currently known.

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Section: λ-Induced Accelerated Expansion and Stabilisation Of Fluidsmentioning

confidence: 53%

Section: λ-Induced Accelerated Expansion and Stabilisation Of Fluidsmentioning

confidence: 81%

Slowly expanding stable dust spacetimes

Fajman,

Ofner,

Wyatt

2021

Preprint

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“…For a global existence result in spherical symmetry without necessarily small (but strongly outgoing) initial data cf. [20]. Note that, for initial data with generic momenta, a smallness assumption is nevertheless necessarily required since the massless system does possess steady states for sufficiently large data [2].…”

Section: The Massless Einstein-vlasov Systemmentioning

confidence: 99%

“…On the other hand, shock formation can be avoided in the presence of expansion[19,21,37,40,41]. 2 This is a small abuse of language, since the particles have no mass here.…”

mentioning

confidence: 99%

Asymptotic Stability of Minkowski Space-Time with Non-compactly Supported Massless Vlasov Matter

Bigorgne

Fajman

Joudioux

et al. 2021

Arch Rational Mech Anal

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We prove the global asymptotic stability of the Minkowski space for the massless Einstein–Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov field in space or the momentum variables are required. In fact, the initial decay in v is optimal. The present proof is based on vector field and weighted vector field techniques for Vlasov fields, as developed in previous work of Fajman, Joudioux, and Smulevici, and heavily relies on several structural properties of the massless Vlasov equation, similar to the null and weak null conditions. To deal with the weak decay rate of the metric, we propagate well-chosen hierarchized weighted energy norms which reflect the strong decay properties satisfied by the particle density far from the light cone. A particular analytical difficulty arises at the top order, when we do not have access to improved pointwise decay estimates for certain metric components. This difficulty is resolved using a novel hierarchy in the massless Einstein–Vlasov system, which exploits the propagation of different growth rates for the energy norms of different metric components.

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“…It is important to note that the Fuchsian techniques we use are based on solving a Cauchy problem and not a singular initial value problem, which is where Fuchsian methods have been traditionally employed. The use of techniques relying on the Fuchsian formulation of the evolution equations to obtain global existence results for Cauchy problems was initiated in [42], and since then, this method has been further developed and employed in a variety of settings to establish the global existence of solutions to Cauchy problems for various field theories [43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant

Ames

Beyer

Isenberg

et al. 2022

Phil. Trans. R. Soc. A.

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We prove the nonlinear stability of the asymptotic behaviour of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarized T 2 -symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant Λ . This stability result generalizes the results proven in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T 2 -symmetric vacuum spacetimes. Ann. Henri Poincaré . ( doi:10.1007/s00023-021-01142-0 )), which focus on the Λ = 0 case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for Λ = 0 , the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarized T 2 -symmetric vacuum solutions than those considered in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T 2 -symmetric vacuum spacetimes. Ann. Henri Poincaré . ( doi:10.1007/s00023-021-01142-0 )) and Fournodavlos G et al. (2020 Stable Big Bang formation for Einstein’s equations: the complete sub-critical regime . Preprint. ( http://arxiv.org/abs/2012.05888 )). Our results establish that the areal time coordinate takes all values in ( 0 , T 0 ] for some T 0 > 0 , for certain families of polarized T 2 -symmetric solutions with cosmological constant. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.

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Stabilizing Relativistic Fluids on Spacetimes with Non-Accelerated Expansion

Cited by 31 publications

References 20 publications

Slowly expanding stable dust spacetimes

Slowly expanding stable dust spacetimes

Asymptotic Stability of Minkowski Space-Time with Non-compactly Supported Massless Vlasov Matter

Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant

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