Related papers: Light-ring pairs from $A$-discriminantal varieties
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
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…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices…
It has been known classically that a star with an ergoregion but no event horizon is unstable to the emission of scalar, electromagnetic and gravitational waves. This classical ergoregion instability is characterized by complex frequency…
We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and…
We introduce and study the so-called {\it weakly $\sqrt{J}U$ rings} (hereafter abbreviated as {\it $W\sqrt{J}U$ rings} for short), in which every unit is of the form $j+1$ or $j-1$ for some $j$ in $\sqrt{J(R)} : = \{x \in R : x^n \in J(R)…
A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation.…
If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz…
Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present…
Black holes binaries support unstable orbits at very close separations. In the simplest case of geodesics around a Schwarzschild black hole the orbits, though unstable, are regular. Under perturbation the unstable orbits can become the…
We present analytical solutions of the geodesic equations of test particles and light in the five dimensional singly spinning black ring spacetime for special cases, since it does not appear possible to separate the Hamilton-Jacobi-equation…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
We construct dark energy stars with Chaplygin-type equation of state (EoS) in the presence of anisotropic pressure within the framework of Einstein gravity. From the classification established by Iyer et al. [Class. Quantum Grav. 2, 219…
The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
Ring galaxies are amazing objects exemplified by the famous case of the Hoag's Object. Here the mass of the central galaxy may be comparable to the mass of the ring, making it a difficult case to model mechanically. In a previous paper, it…
We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli…