General-relativistic approach to the nonlinear evolution of collisionless matter

Journal Article · Mon Feb 15 00:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1311· OSTI ID:6819239

Matarrese, S; Pantano, O ^[1]; Saez, D ^[2]

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1. Dipartimento di Fisica Galileo Galilei,'' Universita di Padova, via Marzolo 8, I-35131 Padova (Italy)
2. Departamento de Fisica Teorica, Universidad de Valencia, Burjassot, Valencia (Spain)

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 approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian form at different times, can be traced back to the Eulerian picture by solving supplementary first-order differential equations for the relative position vectors of neighboring fluid elements. Similarly to the Zel'dovich approximation, in our approach the evolution of each fluid element is completely determined by the local initial conditions and can be independently followed up to the time when it enters a multistream region. Unlike the Zel'dovich approximation, however, our approach is correct also in three dimensions (except for the possible role of gravitational waves). The accuracy of our numerical procedure is tested by integrating the nonlinear evolution of a spherical perturbation in an otherwise spatially flat Friedmann-Robertson-Walker universe and comparing the results with the exact Tolman-Bondi solution for the same initial profile. An exact solution for the planar symmetric case is also given, which turns out to be locally identical to the Zel'dovich solution.

• OSTI ID: 6819239
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 47:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGY
NONLINEAR PROBLEMS
GENERAL RELATIVITY THEORY
ALGORITHMS
EINSTEIN FIELD EQUATIONS
GAUGE INVARIANCE
HUBBLE EFFECT
LIGHT CONE
MATTER
THREE-DIMENSIONAL CALCULATIONS
UNIVERSE
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
INVARIANCE PRINCIPLES
MATHEMATICAL LOGIC
SPACE-TIME
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)