Related papers: Gravitational Dynamics of Cold Matter using the De…
This paper reviews the essential physics of gravitational instability in a Robertson-Walker background spacetime. Three approaches are presented in a pedagogical manner, based on (1) the Eulerian fluid equations, (2) the Lagrangian…
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 gradient tensors. Borrowing results from…
We derive the evolution equations for the electric and magnetic parts of the Weyl tensor for cold dust from both general relativity and Newtonian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the…
The irreducible decomposition technique is applied to the study of classical models of metric-affine gravity (MAG). The dynamics of the gravitational field is described by a 12-parameter Lagrangian encompassing a Hilbert-Einstein term,…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
We propose a new theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct the simplest dynamical Lagrangian density that is entirely composed from the connection,…
Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
In an interesting recent paper on the growth of inhomogeneity through the effect of gravity [1], Bertschinger and Hamilton derive equations for the electric and magnetic parts of the Weyl tensor for cold dust for both General Relativity and…
In a spatially flat \ Friedmann--Lema\^{\i}tre--Robertson--Walker background space we consider a scalar-torsion gravitational model which has similar properties with the dilaton theory. This teleparallel model is invariant under a discrete…
We discuss the gravitational collapse of spherical compact objects in the background of $f(R,T,Q)$ theory, where $R$ represent the Ricci scalar, $T$ is the trace of energy momentum tensor while $Q\equiv R_{\mu\nu}T^{\mu\nu}$, and…
A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time…
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
The paper reports the recent results on application and extension of the matrix formulation of lagrangian hydrodynamic equations. The matrix approach is based on the notion of continuous deformation of infinitesimal material elements and…
Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling collisionless systems. We introduce a new…