642 research outputs found
Gravitomagnetic Accelerators
We study a simple class of time-dependent rotating Ricci-flat cylindrically
symmetric spacetime manifolds whose geodesics admit gravitomagnetic jets. The
helical paths of free test particles in these jets up and down parallel to the
rotation axis are analogous to those of charged particles in a magnetic field.
The jets are attractors. The jet speed asymptotically approaches the speed of
light. In effect, such source-free spacetime regions act as "gravitomagnetic
accelerators".Comment: 4 pages, 2 figures; v2: reference added; v3: slightly expanded
version accepted for publication in Phys. Lett.
Resonance Behavior and Partial Averaging in a Three-Body System with Gravitational Radiation Damping
In a previous investigation, a model of three-body motion was developed which
included the effects of gravitational radiation reaction. The aim was to
describe the motion of a relativistic binary pulsar that is perturbed by a
third mass and look for resonances between the binary and third mass orbits.
Numerical integration of an equation of relative motion that approximates the
binary gives evidence of such resonances. These resonances are defined
for the present purposes by the resonance condition, , where
and are relatively prime integers and and are the
angular frequencies of the binary orbit and third mass orbit, respectively. The
resonance condition consequently fixes a value for the semimajor axis of
the binary orbit for the duration of the resonance because of the Kepler
relationship . This paper outlines a method of averaging
developed by Chicone, Mashhoon, and Retzloff which renders a nonlinear system
that undergoes resonance capture into a mathematically amenable form. This
method is applied to the present system and one arrives at an analytical
solution that describes the average motion during resonance. Furthermore,
prominent features of the full nonlinear system, such as the frequency of
oscillation and antidamping, accord with their analytically derived formulae.Comment: 19 pages, 4 Postscript figure
Gravitational Radiation Damping and the Three-Body Problem
A model of three-body motion is developed which includes the effects of
gravitational radiation reaction. The radiation reaction due to the emission of
gravitational waves is the only post-Newtonian effect that is included here.
For simplicity, all of the motion is taken to be planar. Two of the masses are
viewed as a binary system and the third mass, whose motion will be a fixed
orbit around the center-of-mass of the binary system, is viewed as a
perturbation. This model aims to describe the motion of a relativistic binary
pulsar that is perturbed by a third mass. Numerical integration of this
simplified model reveals that given the right initial conditions and parameters
one can see resonances. These (m,n) resonances are defined by the resonance
condition, , where and are relatively prime integers
and and are the angular frequencies of the binary orbit and
third mass orbit, respectively. The resonance condition consequently fixes a
value for the semimajor axis of the binary orbit for the duration of the
resonance; therefore, the binary energy remains constant on the average while
its angular momentum changes during the resonance.Comment: 16 pages, 3 Postscript figures, to appear in MNRA
On the Ionization of a Keplerian Binary System by Periodic Gravitational Radiation
The gravitational ionization of a Keplerian binary system via normally
incident periodic gravitational radiation of definite helicity is discussed.
The periodic orbits of the planar tidal equation are investigated on the basis
of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser
theory to the question of gravitational ionization is elucidated, and it is
conjectured that the process of ionization is closely related to the Arnold
diffusion of the perturbed system.Comment: 19 pages, REVTEX Style, To appear in JM
Tidal Dynamics in Kerr Spacetime
The motion of free nearby test particles relative to a stable equatorial
circular geodesic orbit about a Kerr source is investigated. It is shown that
the nonlinear generalized Jacobi equation can be transformed in this case to an
autonomous form. Tidal dynamics beyond the critical speed c/sqrt(2) is studied.
We show, in particular, that a free test particle vertically launched from the
circular orbit parallel or antiparallel to the Kerr rotation axis is tidally
accelerated if its initial relative speed exceeds c/sqrt(2). Possible
applications of our results to high-energy astrophysics are briefly mentioned.Comment: 15 pages, 3 figures; v2: slightly expanded version accepted for
publication in CQ
Delay Equations and Radiation Damping
Starting from delay equations that model field retardation effects, we study
the origin of runaway modes that appear in the solutions of the classical
equations of motion involving the radiation reaction force. When retardation
effects are small, we argue that the physically significant solutions belong to
the so-called slow manifold of the system and we identify this invariant
manifold with the attractor in the state space of the delay equation. We
demonstrate via an example that when retardation effects are no longer small,
the motion could exhibit bifurcation phenomena that are not contained in the
local equations of motion.Comment: 15 pages, 1 figure, a paragraph added on page 5; 3 references adde
Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves
The problem of minimal distortion bending of smooth compact embedded
connected Riemannian -manifolds and without boundary is made precise
by defining a deformation energy functional on the set of
diffeomorphisms \diff(M,N). We derive the Euler-Lagrange equation for
and determine smooth minimizers of in case and are simple closed
curves.Comment: Typos corrected to match the final version of the paper, which has
appeared in Opuscula Mathematica in January, 200
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