Journal ArticleDOI
Special relativity in general relativity
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In this article, the EIH Lagrangian is recovered by making a Lorentz transformation, followed by a canonical transformation and an appropriate symmetrization in the two masses.Abstract:
Starting from the metric in harmonic coordinates for a test particle m1 around a heavy particle m2(m2≫m1) at rest, the EIH Lagrangian is recovered by making a Lorentz transformation, followed by a canonical transformation and an appropriate symmetrization in the two masses. This raises the question of a special relativity content in general relativity, a feature not directly implied by the general covariance.read more
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Momentum and angular momentum of two gravitating particles
TL;DR: In this paper, the authors obtained the acceleration, momentum and angular momentum for two gravitating particles to the first order in G. As "criterial" conditions for the determination of the acceleration they used the Lorentz invariant equations obtained by Havas and Goldberg, (1962).
Journal ArticleDOI
Slow motion approximation in predictive relativistic mechanics. I. Approximated dynamics up to order c−4
J. Martin,J. L. Sanz +1 more
TL;DR: In this article, the most general two-body system relativistic invariant having a Newtonian limit up to c−4 order was obtained, which includes the scalar, gravitational, and other well-known dynamics.
Journal ArticleDOI
Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe
TL;DR: In this article, it was shown that these long range interactions imply Mach's principle, provided the universe has the critical density, and that mass is renormalized, and the higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.
Journal ArticleDOI
Stability of Solutions of Stochastic Functional Differential Equations with an Infinite Previous History and Poisson Switchings. II
E. V. Yasinskii,V. K. Yasinskii +1 more
TL;DR: In this article, the stability of the stochastic "dangling spider" model was investigated and the second Lyapunov method was substantiated for stochastically differential functional equations with the whole previous history.
Posted Content
Gravitational Lagrangians, Mach's principle, and the equivalence principle in an expanding universe
TL;DR: In this article, the equivalence principle was invoked to renormalize the masses to the same values as the inertial masses in a homogeneous isotropic expanding universe and the Lagrangian was found to be consistent with Mach's principle when the density is the critical density and inertial mass is suitably renormalized.
References
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Journal ArticleDOI
The theory of space, time and gravitation
TL;DR: In this article, a key input circuit is described where the key input signal is serialized and applied directly and through a circulating register working with a certain delay time to one gate for transmitting the direct input signal and to another gate to transmit the output of the register utilizing the other signal as an inhibitation signal.
Journal ArticleDOI
The Gravitational equations and the problem of motion
TL;DR: In this article, it was shown that the relativistic equations of gravitation for empty space are sufficient to determine the motion of matter represented as point singularities of the field.
Journal ArticleDOI
Instantaneous Action‐at‐a‐Distance in Classical Relativistic Mechanics
TL;DR: The possibility of describing orbits in classical relativistic mechanics in instantaneous action-at-a-distance fashion by second-order differential equations (as in Newton's gravitational theory) was investigated with particular emphasis on the two-body problem of classical electrodynamics.