# 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…

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## References

SHOWING 1-10 OF 85 REFERENCES

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

- Physics
- 1992

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

- Physics
- 1998

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.

- PhysicsPhysical review. D, Particles and fields
- 1993

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

- PhysicsClassical and Quantum Gravity
- 1998

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

- Physics, Mathematics
- 2001

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

- Physics
- 1996

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

- Physics
- 1993

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

- Physics
- 1993

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

- Physics
- 1992

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

- Physics
- 1999

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…