Consistency of dust solutions with div<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mn /></mml:math>

Maartens, Roy; Lesame, William M.; Ellis, George

doi:10.1103/physrevd.55.5219

Cited by 32 publications

(46 citation statements)

References 6 publications

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“…This arises from the time evolution of (27), which must also be satisfied. Using the identities (A5) and (A7), the propagation equations (19) and (21), and the constraint equations (23) and (24), we find that †Ċ…”

Section: Anti-newtonian Models (Ementioning

confidence: 99%

Newtonian-like and anti-Newtonian universes

Maartens

Lesame

Ellis

1998

Class. Quantum Grav.

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In an irrotational dust universe, the locally free gravitational field is covariantly described by the gravito-electric and gravito-magnetic tensors E ab and H ab . In Newtonian theory, H ab = 0 and E ab is the tidal tensor. Newtonian-like dust universes in general relativity (i.e. with H ab = 0, often called 'silent') have been shown to be inconsistent in general and unlikely to extend beyond the known spatially homogeneous or Szekeres examples. Furthermore, they are subject to a linearization instability. Here we show that 'anti-Newtonian' universes, i.e. with purely gravito-magnetic field, so that E ab = 0 = H ab , are also subject to severe integrability conditions. Thus these models are inconsistent in general. We show also that there are no anti-Newtonian spacetimes that are linearized perturbations of Robertson-Walker universes. The only E ab = 0 = H ab solution known to us is not a dust solution, and we show that it is kinematically Gödel-like but dynamically unphysical.PACS numbers: 0420, 9880, 9530 IntroductionIrrotational dust spacetimes are characterized by vanishing pressure (p = 0) ‡ and vorticity (ω a = 0), and positive energy density (ρ > 0). They are important arenas for studying both the late universe [1,2] and gravitational collapse models [3]. Apart from the spatially homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) case, which is characterized by vanishing shear (σ ab = 0), these spacetimes have non-zero shear and non-zero locally free gravitational field. This field is represented by the irreducible electric and magnetic parts E ab and H ab of the Weyl tensor (see [4] for a covariant analysis of local freedom in the gravitational field). ‡ It is implicit that the anisotropic stress π ab and the energy flux q a also vanish. § A weaker covariant condition for the absence of gravitational radiation is that the spatial curls (defined below) of E ab and H ab must vanish [7,8,4].

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Section: Anti-newtonian Models (Ementioning

confidence: 99%

Newtonian-like and anti-Newtonian universes

Maartens

Lesame

Ellis

1998

Class. Quantum Grav.

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“…ρ = 0 = p, then the similarity of the two sets of equations is even more apparent, and only the tensor shear coupling in the case of gravity lacks a direct electromagnetic analogue. (Note that these shear coupling terms govern the possibility of simultaneous diagonalization of the shear and E ab , H ab in tetrad formulations of general relativity [41,42]. )…”

Section: The Bianchi Identities and Nonlinear Dualitymentioning

confidence: 99%

Gravito-electromagnetism

Maartens

Bassett

1998

Class. Quantum Grav.

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353

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Abstract.We develop and apply a fully covariant 1 + 3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. We construct the super-energy density and super-Poynting vector of the gravitational field as natural U (1) group invariants, and derive their super-energy conservation equation. A covariant approach to gravito-electric/magnetic monopoles is also presented.

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“…Apart from these equations, one also need to satisfy the spatial constraints. However, the spatial constrains need only be satisfied at the initial instant, as they are conserved by the above evolution equations [4,16]. Setting up the initial condition is thus important and non-trivial task.…”

Section: A Nonlinear Relativistic Evolution -The Silent Universe Appmentioning

confidence: 99%

Environment dependence of the growth of the most massive objects in the Universe

Bolejko

Ostrowski

2019

Phys. Rev. D

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This paper investigates the growth of the most massive cosmological objects. We utilize the Simsilun simulation, which is based on the approximation of the silent universe. In the limit of spatial homogeneity and isotropy the silent universes reduce to the standard FLRW models. We show that within the approximation of the silent universe the formation of the most massive cosmological objects differs from the standard background-dependent approaches. For objects with masses above 10 15 M⊙ the effect of spatial curvature (overdense regions are characterized by positive spatial curvature) leads to measurable effects. The effect is analogous to the effect that the background cosmological model has on the formation of these objects (i.e. the higher matter density and spatial curvature the faster the growth of cosmic structures). We measure this by the means of the mass function and show that the mass function obtained from the Simsilun simulation has a higher amplitude at the high-mass end compared to standard mass function such as the Press-Schechter or the Tinker mass function. For comparison, we find that the expected mass of most massive objects using the Tinker mass function is 4.4 +0.8 −0.6 × 10 15 M⊙, whereas for the Simsilun simulation is 6.3 +1.0 −0.8 × 10 15 M⊙. We conclude that the nonlinear relativistic effects could affect the formation of the most massive cosmological objects, leading to a relativistic environment-dependence of the growth rate of the most massive clusters.

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Consistency of dust solutions with divH=0

Cited by 32 publications

References 6 publications

Newtonian-like and anti-Newtonian universes

Newtonian-like and anti-Newtonian universes

Gravito-electromagnetism

Environment dependence of the growth of the most massive objects in the Universe

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