Related papers: Sachs equations and plane waves III: Microcosms
We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The…
The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetime. The class of pp-wave metrics together with…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
It is investigated the gravitational waves phenomena in the geometric scalar theory of gravity (GSG), a class of theories such that gravity is described by a single scalar field. The associated physical metric describing the spacetime is…
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…
We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a…
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the proper time \tau…
The scalar induced gravitational waves (SIGWs) is a useful tool to probe the physics in the early universe. To study inflationary models with this tool, we need to know how the waveform of SIGWs is related to the shape of the scalar power…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the…
We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…
A phenomenological model of an ideal fluid with a scalar charge is formulated, on the basis of which a model with a neutral fluid and a vacuum-field model with rules of transition between them are constructed. A qualitative analysis of the…
Set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass {\wp} function and the Kleinian {\sigma} function. Using conserved…
Generalised Hagedorn wave packets appear as exact solutions of Schr\"odinger equations with quadratic, possibly complex, potential, and are given by a polynomial times a Gaussian. We show that the Wigner transform of generalised Hagedorn…
Let K be a non-Archimedean local field with the normalized absolute value $|\cdot |$. It is shown that a ``plane wave'' $f(t+\omega_1 x_1+... +\omega_nx_n)$, where f is a Bruhat-Schwartz complex-valued test function on K, $(t,x_1,...,…
We develop a correspondence between the orbits of the group of linear symplectomorphisms of a real finite dimensional symplectic vector space in the complex Lagrangian Grassmannian and the Grassmannians of linear subspaces of the real…
The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map…
We analyze the d'Alembert equation in the Goedel-type spacetimes with spherical and Lobachevsky sections (with sufficiently rapid rotation). By separating the $t$ and $x_3$ dependence we reduce the problem to a group-theoretical one. In the…
Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einsteins Field equations for vacuum, yields the Schwarzschild Metric as the unique solution,…
A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…