Related papers: Pedal coordinates and free double linkage
We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…
It was shown that pedal coordinates provides natural framework in which to study force problems of classical mechanics in the plane. A trajectory of a test particle under the influence of central and Lorentz-like forces can be translated…
We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with the singularity…
We present detailed physics analyses of two different 4+1-dimensional asymptotically flat vacuum black hole solutions with spin in two independent planes: the doubly spinning black ring and the bicycling black ring system ("bi-rings"). The…
A non-extreme dilatonic charged (by two ``color electric'' charges) black hole solution is examined within a four-dimensional gravity model that incorporates two scalar (dilaton) fields and two Abelian vector fields. The scalar and vector…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely defined circumcircles. The solution encapsulates two generalizations, one of which uses a powerful projective result…
With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting…
These lectures describe how to study the geometry of some black holes without the use of coordinates.
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…
In this paper, we study several topics on pedal polygons. First, we prove the existence for pedal centers of triangles in a new way. From its proof, we find that the sum of area of outer and inner polygons is invariant under rotation.…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits,…
Based on the consideration of potential energy of the di-black-hole as a function of mass asymmetry (transfer) collective coordinate, the possibility of matter transfer between the black holes in a binary system is investigated. The…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
This paper investigates the trajectories of light beams in a Kerr metric, which describes the gravitational field in the neighborhood of a rotating black hole. After reduction by cyclic coordinates, this problem reduces to analysis of a…
We study circular orbits that are tilted with respect to the equatorial plane around a Kerr black hole. We write the equations for the parameters of a tilted circular orbit in terms of the orbit's radius and the Carter constant, or…
We describe a numerical grid generating procedure to construct new classes of orthogonal coordinate systems that are specially adapted to binary black hole spacetimes. The new coordinates offer an alternative approach to the conventional…
This work deals with the formation of black hole in bidimensional dilaton gravity coupled to scalar matter fields. We investigate two scalar matter systems, one described by a sixth power potential and the other defined with two scalar…