Relativistic approach to nonlinear peculiar velocities and the Zeldovich approximation

@article{Ellis2002RelativisticAT,
  title={Relativistic approach to nonlinear peculiar velocities and the Zeldovich approximation},
  author={George F R Ellis and Christos G. Tsagas},
  journal={Physical Review D},
  year={2002},
  volume={66},
  pages={124015}
}
We study the peculiar motion of nonrelativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our two-frame formalism facilitates the study of the nonlinear kinematics of the matter, as the latter decouples from the background expansion and starts to ``turn around'' and collapse. Applied to second perturbative order, our equations provide a fully covariant… 

Figures from this paper

Large-scale peculiar velocity fields: Newtonian vs relativistic treatment

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within the framework of Newtonian gravity and then compare our results to those of the corresponding

Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids

We extend the general relativistic Lagrangian perturbation theory, recently developed for the formation of cosmic structures in a dust continuum, to the case of model universes containing a single

Zel'dovich approximation and general relativity

We show how the Zel'dovich approximation and the second-order displacement field of Lagrangian perturbation theory can be obtained from a general relativistic gradient expansion incold dark matter

Relativistic approach to the kinematics of large-scale peculiar motions

We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the "real" observers that move along with the peculiar flow,

ON THE LAGRANGIAN PERTURBATION THEORY OF STRUCTURE FORMATION IN GENERAL RELATIVITY

In this thesis we focus on two different problems in the study of the formation and evolution of large scale structure using the Lagrangian perturbation approach. First, we study the effects of

Lagrangian theory of structure formation in relativistic cosmology: Lagrangian framework and definition of a nonperturbative approximation

In this paper, we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a

Covariant Evolution of Gravitoelectromagnetism

The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann

Peculiar Raychaudhuri equation

Peculiar motions are commonplace in the universe. Our local group of galaxies, for example, drifts relative to the Hubble flow at about 600 km/sec. Such bulk flows are believed to fade away as we

References

SHOWING 1-10 OF 85 REFERENCES

Lagrangian theory of gravitational instability of Friedman-Lemaitre cosmologies and the 'Zel'dovich approximation'

The aim of this paper is to clarify the connection between the so-called Zel'dovich approximation and perturbative solutions of the Euler-Poisson system for the motion of a self-gravitating dust

Covariant velocity and density perturbations in quasi-Newtonian cosmologies

Recently a covariant approach to cold matter universes in the zero-shear hypersurfaces (or longitudinal) gauge has been developed. This approach reveals the existence of an integrability condition,

General-relativistic approach to the nonlinear evolution of collisionless matter.

A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the

Quasi-Newtonian dust cosmologies

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated

General relativistic analysis of peculiar velocities

We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our

Post-Newtonian Cosmological Dynamics in Lagrangian coordinates

We study the non-linear dynamics of self-gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written

Gravitational Instability of Cold Matter

We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity

Lagrangian theory of gravitational instability of Friedman–Lemaître cosmologies – second-order approach: an improved model for non-linear clustering

A large class of solutions for second-order irrotational perturbations is derived in the framework of the Lagrangian theory of gravitational instability of a homogeneous and isotropic universe

Weakly nonlinear gravitational instability for arbitrary Omega

The weakly nonlinear evolution of particle trajectories in Friedmann-Lemaitre models with zero cosmological constant is investigated. The matter is assumed to be a nonrelativistic pressureless fluid.

Cosmic microwave background anisotropies: nonlinear dynamics

We develop a new approach to local nonlinear effects in cosmic microwave background anisotropies, and discuss the qualitative features of these effects. New couplings of the baryonic velocity to
...