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

Friedman, Yaakov; Stav, Shmuel

doi:10.1209/0295-5075/126/29001

Cited by 2 publications

(11 citation statements)

References 13 publications

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“…with φ(r) defined by (23). Dividing this equation by c 2 dτ 2 and using the definition (7) of τ, we obtain…”

Section: Newtonian Limit Consequence For the Metric Of The Field Of Amentioning

confidence: 99%

“…Consider a gravitational field generated by a spherically symmetric body of mass M positioned at the origin of our inertial frame K. The motion of an object or planet in RND is by a geodesic with respect to the metric (16), where φ(r) is defined by (23). We may assume that the trajectory is in a plane determined by the initial position of the object and its initial velocity and this plane is passing through the origin.…”

Section: Trajectories Of Planetary Motion In a Static Spherically Symentioning

confidence: 99%

“…Thus, in RND it is impossible to split the energy into kinetic and potential energies. It is known [6,9,23] that the dynamics following from the metric (34), with φ defined by (23), satisfies Einstein's field equations and passes the following classical tests of GR:…”

Section: Trajectories Of Planetary Motion In a Static Spherically Symentioning

confidence: 99%

“…From (23) and (36), conservation of the t-momentum on a geodesic trajectory under RND is expressed as…”

Section: Distinctions Between Rn D and Gr Dynamicsmentioning

confidence: 99%

“…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%

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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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“…with φ(r) defined by (23). Dividing this equation by c 2 dτ 2 and using the definition (7) of τ, we obtain…”

Section: Newtonian Limit Consequence For the Metric Of The Field Of Amentioning

confidence: 99%

Section: Trajectories Of Planetary Motion In a Static Spherically Symentioning

confidence: 99%

Section: Trajectories Of Planetary Motion In a Static Spherically Symentioning

confidence: 99%

“…From (23) and (36), conservation of the t-momentum on a geodesic trajectory under RND is expressed as…”

Section: Distinctions Between Rn D and Gr Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relativistic Gravitation Based on Symmetry

Friedman

2020

Symmetry

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Testing Relativistic Time Dilation beyond the Weak-Field Post-Newtonian Approximation

Friedman

Yudkin

2020

Symmetry

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In General Relativity, the gravitational field of a spherically symmetric non-rotating body is described by the Schwarzschild metric. This metric is invariant under time reversal, which implies that the power series expansion of the time dilation contains only even powers of v / c . The weak-field post-Newtonian approximation defines the relativistic time dilation of order ϵ (or of order ( v / c ) 2 ) of the small parameter. The next non-zero term of the time dilation is expected to be of order ϵ 2 , which is impossible to measure with current technology. The new model presented here, called Relativistic Newtonian Dynamics, describes the field with respect to the coordinate system of a far-removed observer. The resulting metric preserves the symmetries of the problem and satisfies Einstein’s field equations, but predicts an additional term of order ϵ 3 / 2 for the time dilation. This term will cause an additional periodic time delay for clocks in eccentric orbits. The analysis of the gravitational redshift data from the Galileo satellites in eccentric orbits indicates that, by performing an improved satellite mission, it would be possible to test this additional time delay. This would reveal which of the coordinate systems and which of the above metrics are real. In addition to the increase of accuracy of the time dilation predictions, such an experiment could determine whether the metric of a spherically symmetric body is time reversible and whether the speed of light propagating toward the gravitating body is the same as the speed propagating away from it. More accurate time dilation and one-way speed of light formulas are important for astronomical research and for global positioning systems.

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

Cited by 2 publications

References 13 publications

Relativistic Gravitation Based on Symmetry

Relativistic Gravitation Based on Symmetry

Testing Relativistic Time Dilation beyond the Weak-Field Post-Newtonian Approximation

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