Related papers: Peeling or not peeling -- is that the question ?
In self-consistent N-body simulations of collisionless systems, gravitational interactions are modified on small scales to remove singularities and simplify the task of numerically integrating the equations of motion. This `gravitational…
Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.
We discuss on different issues pertaining the theory of gravity, which pose some unresolved fundamental questions. First we tackle the problem of observers in general relativity, with particular emphasis in tilted observers. We explain why…
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art…
We comment on the methods and the conclusion of Ref. [1], "Does gravitational confinement sustain flat galactic rotation curves without dark matter?" The article employs two methods to investigate whether non-perturbative corrections from…
The gravitational collapse of spherical, barotropic perfect fluids is analyzed here. For the first time, the final state of these systems is studied without resorting to simplifying assumptions - such as self-similarity - using a new…
We make a systematic investigation of the generic properties of static, spherically symmetric, asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self-gravitating real scalar field.…
Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…
The notion of sterile neutrinos is discussed. The schemes of mixing of four massive neutrinos, which imply the existence of sterile neutrinos, are briefly considered. Several model independent methods that allow to reveal possible…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous…
Conditions under which gravity coupled to self interacting scalar field determines singularity formation are found and discussed. It is shown that, under a suitable matching with an external space, the boundary, if collapses completely, may…
We propose a definition of asymptotically flat spacetimes that is consistent with both null infinities and compatible with known properties of gravitational scattering, incoming and outgoing radiation, and interactions with matter. For this…
This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behaviour with convergence to a limiting…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass problem, showing how considerations of an apparently insignificant and practically unimportant…
In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
I discuss possible implications a symmetry relating gravity with antigravity might have for smoothing out of the cosmological constant puzzle. For this purpose, a very simple model with spontaneous symmetry breaking is explored, that is…