Related papers: Static spacetimes with prescribed multipole moment…

Assuming only a smooth and slow change of spacetime dimensionality at large scales, we find, in a background- and model-independent way, the general profile of the Hausdorff and the spectral dimension of multiscale geometries such as those…

Our aim is to prove Liouville type theorems for the three dimensional steady-state Navier-Stokes equations provided the velocity field belongs to some Lorentz spaces. The corresponding statement contains several known results as a…

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial…

We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We…

The gravitational and electromagnetic multipole moments of the charged rotating disc of dust, which is an axisymmetric, stationary solution of the Einstein-Maxwell equations in terms of a post-Newtonian expansion, are calculated and…

In this paper we work out a multiverse scenario whose physical characteristics enable us to advance the following the conjecture that whereas the physics of particles and fields is confined to live in the realm of the whole multiverse…

A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any…

We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the…

Geroch's theorem about the splitting of globally hyperbolic spacetimes is a central result in global Lorentzian Geometry. Nevertheless, this result was obtained at a topological level, and the possibility to obtain a metric (or, at least,…

In this paper, we generalize a positive recurrence criterion for multidimensional discrete-time Markov chains over countable state spaces due to Rosberg (JAP, Vol. 17, No. 3, 1980). We revisit the stability analysis of well known…

The multipole moments are defined as the multipole expansion coefficients of the gravitational field at infinity. In Newtonian gravity, the multipole moments are determined by the source distribution -- the multipole integrals of the…

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between…

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…

We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum…

The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

It is known from the work of Czubak that the space-time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in $H^s(\mathbb{R}^2)$ for $s>1/4$. Here we prove local well-posedness for arbitrary initial data in…

We show explicitly that there is particle creation in a static spacetime. This is done by studying the field in a coordinate system based on a physical principle which has recently been proposed. There the field is quantized by decomposing…

For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…