Relativity from the geometrization of Newtonian dynamics

Friedman, Yaakov; Scarr, Tzvi

doi:10.1209/0295-5075/125/49001

Cited by 2 publications

(4 citation statements)

References 35 publications

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“…-Consider radial motion. The trajectory of this motion is optimized with respect to the function L(x,ẋ), which in this case is L t, r,ṫ,ṙ = mc g 00 (r)c 2ṫ2 − g 11 (r)ṙ 2 − 2cg 01 (r)ṫṙ, (6) where the · denotes differentiation by τ . The Euler-Lagrange equation for the r coordinate is…”

Section: P-1mentioning

confidence: 99%

“…Its geodesic motion is obtained by optimizing with respect to the Lagrangian function L(x, ẋ) = mc ds dτ (see [5]). As shown in [6], p. 3, since the Lagrangian does not depend on ϕ and the angular momentum is conserved on any geodesic trajectory, one obtains that l(r) ≡ 1. Thus, the metric is characterized by g 00 (r), g 01 (r) and g 11 (r).…”

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confidence: 91%

“…The results presented here are based on the ideas of relativistic Newtonian dynamics [5] and [6] applied to a general, spherically symmetric gravitational field.…”

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confidence: 99%

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New metrics of a spherically symmetric gravitational field passing classical tests of general relativity

Friedman¹,

Stav²

2019

EPL

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A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have g01(r) = 0. The Newtonian limit uniquely defines g00(r). Geodesic motion under such metric exactly reproduces the precession of a planetary orbit, periastron advance of a binary, deflection of light and Shapiro time delay if the determinant of the time-radial parts of the metric is −1. In this model, the total time for a radial round trip of light is as in the Schwarzschild model, but it allows for light rays to have different speeds propagating toward or from the massive object. The value of g01(r) could be obtained by measuring these speeds. All of these metrics do satisfy Einstein's field equations.

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Section: P-1mentioning

confidence: 99%

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New metrics of a spherically symmetric gravitational field passing classical tests of general relativity

Friedman¹,

Stav²

2019

EPL

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“…In this paper, we present a Relativistic Newtonian Dynamics (RND) for a gravitational field. An earlier version was developed by the author and others [14][15][16][17][18][19][20][21][22][23]. RND is an attempt to realize Riemann's program for all forces.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Gravitation Based on Symmetry

Friedman

2020

Symmetry

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We present a Relativistic Newtonian Dynamics ( R N D ) for motion of objects in a gravitational field generated by a moving source. As in General Relativity ( G R ), we assume that objects move by a geodesic with respect to some metric, which is defined by the field. This metric is defined on flat lab spacetime and is derived using only symmetry, the fact that the field propagates with the speed of light, and the Newtonian limit. For a field of a single source, the influenced direction of the field at spacetime point x is defined as the direction from x to the to the position of the source at the retarded time. The metric depends only on this direction and the strength of the field at x. We show that for a static source, the R N D metric is of the same form as the Whitehead metric, and the Schwarzschild metric in Eddington–Finkelstein coordinates. Motion predicted under this model passes all classical tests of G R . Moreover, in this model, the total time for a round trip of light is as predicted by G R , but velocities of light and object and time dilation differ from the G R predictions. For example, light rays propagating toward the massive object do not slow down. The new time dilation prediction could be observed by measuring the relativistic redshift for stars near a black hole and for sungrazing comets. Terrestrial experiments to test speed of light predictions and the relativistic redshift are proposed. The R N D model is similar to Whitehead’s gravitation model for a static field, but its proposed extension to the non-static case is different. This extension uses a complex four-potential description of fields propagating with the speed of light.

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Relativity from the geometrization of Newtonian dynamics

Cited by 2 publications

References 35 publications

New metrics of a spherically symmetric gravitational field passing classical tests of general relativity

New metrics of a spherically symmetric gravitational field passing classical tests of general relativity

Relativistic Gravitation Based on Symmetry

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