Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations: Foundations

A transfer matrix-direct integration combined method is proposed, which employs the transfer matrix method to derive the equations of motion of a “characteristic disk,” and uses the direct integration method to determine the critical speeds, modes and unbalance response of a rotor-bearing system, and to analyze its stability. Despite the complexity of the system, the number of governing equations is not greater than eight. For a single-spool rotating system, the number of equations is only four. A transfer matrix for a uniform shaft is derived to consider its distributed mass, moment of inertia and the effect of shearing force. An impedance matrix iteration method is proposed to consider the effect of a complicated bearing-supporting system on the rotor dynamics. Two examples are given, and the results agree satisfactorily with the experiments.

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SPHERICALLY SYMMETRIC AND ROTATING WORMHOLES PRODUCED BY LIGHTLIKE BRANES

International Journal of Modern Physics A ◽

10.1142/s0217751x10047762 ◽

2010 ◽

Vol 25 (07) ◽

pp. 1405-1428 ◽

Cited By ~ 14

Author(s):

EDUARDO GUENDELMAN ◽

ALEXANDER KAGANOVICH ◽

EMIL NISSIMOV ◽

SVETLANA PACHEVA

Keyword(s):

Equations Of Motion ◽

Dynamical Variable ◽

Einstein Equations ◽

Spherically Symmetric ◽

Brane Tension ◽

Small Magnitude ◽

Traversable Wormhole ◽

Particular Solution ◽

Test Objects ◽

Matter Energy

Lightlike p-branes (LL-branes) with dynamical (variable) tension allow simple and elegant Polyakov-type and dual to it Nambu–Goto-like worldvolume action formulations. Here we first briefly describe the dynamics of LL-branes as test objects in various physically interesting gravitational backgrounds of black hole type, including rotating ones. Next we show that LL-branes are the appropriate gravitational sources that provide proper matter energy–momentum tensors in the Einstein equations of motion needed to generate traversable wormhole solutions, in particular, self-consistent cylindrical rotating wormholes, with the LL-branes occupying their throats. Here a major role is being played by the dynamical LL-brane tension which turns out to be negative but may be of arbitrary small magnitude. As a particular solution we obtain traversable wormhole with Schwarzschild geometry generated by a LL-brane positioned at the wormhole throat, which represents the correct consistent realization of the original Einstein–Rosen "bridge" manifold.

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Integrated equations of motion for direct integration methods

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2002.13.5.569 ◽

2002 ◽

Vol 13 (5) ◽

pp. 569-589 ◽

Cited By ~ 8

Author(s):

Shuenn-Yih Chang

Keyword(s):

Equations Of Motion ◽

Direct Integration ◽

Integration Methods

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The solutions of the Einstein equations for uniformly accelerated particles without nodal singularities. II. Self-accelerating particles

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1983.0139 ◽

1983 ◽

Vol 390 (1799) ◽

pp. 411-419 ◽

Cited By ~ 15

Keyword(s):

General Solution ◽

General Theory ◽

Gravitational Radiation ◽

Model Space ◽

Einstein Equations ◽

Multipole Moments ◽

Spatial Infinity ◽

Asymptotic Structure ◽

Rotation Symmetry ◽

Accelerated Particles

Solutions are given representing two independent particles uniformly accelerated in opposite directions; the accelerations are not produced by nodal singularities, which are absent. One solution is constructed from the solution of Bonnor & Swaminarayan ( Z . Phys . 177, 240 (1964)) for two pairs of uniformly accelerated particles by a limiting procedure. Other solutions are obtained by solving the Einstein equations directly. A general solution representing two accelerating particles with arbitrary multipole structure attached to nodal singularities is first given. Then a condition restricting multipole moments is found, and this causes the nodal singularities to disappear. Although solutions of this type do not involve very physical sources, they belong to the best model space-times available today for examining the general theory of the asymptotic structure and the theory of gravitational radiation. Owing to the boost-rotation symmetry, the ADM 4-momentum at spatial infinity vanishes.

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