Related papers: Gravitational softening as a smoothing operation
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
The effective action for quantum gravity coupled to matter contains corrections arising from the functional measure. We analyse the effect of such corrections for anisotropic self-gravitating compact objects described by means of the…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron…
Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
Theory and simulations are used to study collisionless relaxation of a gravitational $N$-body system. It is shown that when the initial one particle distribution function satisfies the virial condition -- potential energy is minus twice the…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
Using the Ricci and scalar curvatures of the configuration manifold of gravitational N-body systems, we study the exponential instability in their trajectories. It is found that the exponentiation time-scale for isotropic Plummer spheres…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
The Garvey-Kelson (GK) relations are powerful algebraic expressions connecting the masses of neighboring atomic nuclei and derived under reasonable physical assumptions. In this contribution we show that these relations are even more…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
A persistent theme in the study of dark energy is the question of whether it really exists or not. It is often claimed hat we are mis-calculating the cosmological model by neglecting the effects associated with averaging over large-scale…
A mass distribution is analyzed in terms of classical gravitational field theory. Newton's law of gravitation is consistently applied on the assumption that the equivalence of energy and mass according to Einstein's theory of relativity is…
In 2D simulations of thin gaseous disks with embedded planets or self-gravity the gravitational potential needs to be smoothed to avoid singularities in the numerical evaluation of the gravitational potential or force. In order to correctly…
Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise,…
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
Spherical dust collapse generally forms a shell focusing naked singularity at the symmetric center. This naked singularity is massless. Further the Newtonian gravitational potential and speed of the dust fluid elements are everywhere much…