Related papers: On Orbit Spaces of Distributive Binary $G$-Spaces
We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…
Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings.…
In this article we consider a restricted orbital counting problem for the action of certain discrete groups on suitable spaces. In particular, we present asymptotics for counting those points in an orbit restricted to a single conjugacy…
The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\"onigsd\"orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and…
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…
Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin…
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
We show that a finite unitary group which has orbits spanning the whole space is necessarily the setwise stabilizer of a certain orbit.
Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$, and $G$ is not metacyclic. Then $G$ always has a regular orbit on $V$ except for a few "small" cases. We completely…
Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space one assigns certain combinatorial invariants: the weight…
The orbit polytope for a finite group G acting linearly and freely on a sphere S is used to construct a cellularized fundamental domain for the action. A resolution of the integers over G results from the associated G-equivariant…
Hyperbolic encounters of compact objects are common interactions in dense environments. During this process a significant amount of gravitational radiation is emitted depending on the parameters of the system. Here we give a parametric…
Most all-sky searches for continuous gravitational waves assume the source to be isolated. In this paper, we allow for an unknown companion object in a long-period orbit and opportunistically use previous results from an all-sky search for…
We present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum…
A binary system composed of an oscillating and rotating coplanar dusty disk and a point mass is considered. The conservative dynamics is treated on the Newtonian level. The effects of gravitational radiation reaction and wave emission are…
We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
Merging compact binaries are the most viable and best studied candidates for gravitational wave (GW) detection by the fully operational network of ground-based observatories. In anticipation of the first detections, the expected…
Invariant functions under the transformations of a compact linear group $G$ acting in $\real^n$ can be expressed in terms of functions defined in the orbit space of $G$. We develop a method to determine the isotropy classes of the orbit…