Related papers: Evolution of angular momentum and center of mass a…
We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark…
In the framework of the quasigroup approach to conservation laws in general relativity, we show how the infinite-parametric Newman-Unti group of asymptotic symmetries can be reduced to the Poincare quasigroup. We compute Noether's charges…
I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
In this work we give a complete picture of how to in a direct simple way define the mass at null infinity in harmonic coordinates in three different ways that we show satisfy the Bondi mass loss law. The first and second way involve only…
We relate Bondi systems near space-like infinity to another type of gauge conditions. While the former are based on null infinity, the latter are defined in terms of Einstein propagation, the conformal structure, and data on some Cauchy…
Chen et al. argued recently that, in Bondi-Sachs space-times, the angular momentum at scri (null infinity) should vary continuously with the position of the cut (but not depend sensitively on its derivatives); they showed that this property…
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change…
The present work is devoted to study the dynamical evolution of the galaxies in scalar-GaussBonnet gravity in relationship with the MOND paradigm. This study is useful for giving meaning to the presence of a new gravitational constant. The…
We study the fate of global symmetries at the late-time boundary of de Sitter space. In anti-de Sitter space, bulk gauge symmetries generally correspond to conserved global currents on the boundary. We show that in de Sitter space such…
For axisymmetric evolution of isolated systems, we prove that there exists a gauge such that the total mass can be written as a positive definite integral on the spacelike hypersurfaces of the foliation and the integral is constant along…
How does one compute the Bondi mass on an arbitrary cut of null infinity $\scri$ when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed…
We have developed a model for the evolution of the Earth-Moon angular momenta, energy dissipation and tidal torque valid for the entire history of the Earth-Moon system. The model is supported by present observational data.
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are…
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…
In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…
We describe conditions assuring that the Kerr--Schild type solutions of Einstein equations with pure radiation fields are asymptotically flat at future null infinity. Such metrics cannot describe ``true'' gravitational radiation from…
We investigate conservation laws of the two-dimensional Zakharov--Kuznetsov (ZK) equation, a natural higher-dimensional and non-integrable extension of the Korteweg--de Vries equation. The ZK equation admits three scalar conserved…
Conservation equations for the mass, linear momentum and energy densities of solitons propagating in finite, infinite and periodic, nonlinear, planar waveguides and governed by the nonlinear Schr\"odinger equation are derived. These…