This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. Aft...

The gravitational collapse of a cylindrically distributed perfect fluid is studied. We assume that the collapsing speed of the fluid is very large and investigate such a situation using recently proposed high-speed approximation scheme. We show that if the value of the pressure divided by the energy density is bounded below by some positive value, the high-speed collapse is necessarily decelera...

We obtain the correct hamiltonian which describes the dynamics of classes of asymptotic open Friedmann-Lemâıtre-Robertson-Walker (FLRW) spacetimes, which includes Tolman geometries. We calculate the surface term that has to be added to the usual hamiltonian of General Relativity in order to obtain an improved hamiltonian with well defined functional derivatives. For asymptotic flat FLRW spaces,...

A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next, following current ideas about the emergence of spacetime, we regard gravitational equipotentials as isoentropic surfaces. Therefore, gravitational entropy i...

Abstract We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel $$f\left( Q\right) $$ f Q -theory. For background geometry we consider Kantowski–Sachs and Locally Rotationally Symmetric Bianchi typ...

This is the first in a series of papers on the construction and validation of a threedimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and convergence of our general relativistic hydrodynamic treatment and its coupling to the spacetime evolutions described by the full set of Einstein equations wi...

We prove the theorem: The necessary and suucient condition for a spherically symmetric spacetime to represent an isothermal perfect uid (barotropic equation of state with density falling oo as inverse square of the curvature radius) distribution without boundary is that it is conformal to the \minimally" curved (gravitation only manifesting in tidal acceleration and being absent in particle tra...

The stability and other physical properties of a class regular black holes, quasiblack electrically charged compact objects are investigated in the present work. obtained by solving Einstein-Maxwell system equations assuming spherical symmetry static spacetime. spacetime is split two regions surface coordinate radius $a$. interior region contains nonisotropic fluid with de Sitter type equation ...

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n(≥ 5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M ≈ M × K with a perfect fluid and a cosmological constant. This is a generalizat...