# Relativistic Gravitation Based on Symmetry

## Abstract

**:**

## 1. Introduction

## 2. The Ideas behind Relativistic Newtonian Dynamics

**Proposition**

**1.**

## 3. Symmetry Consequence for the Metric of the Field of a Static, Spherically Symmetric Source

## 4. Newtonian Limit Consequence for the Metric of the Field of a Static, Spherically Symmetric Source

## 5. Trajectories of Planetary Motion in a Static, Spherically Symmetric Gravitational Field

- (1)
- the anomalous precession of Mercury
- (2)
- the periastron advance of a binary star
- (3)
- gravitational lensing
- (4)
- the Shapiro time delay

## 6. Distinctions between RND and GR Dynamics

## 7. Testing the RND and GR Redshift in Strong Gravitation

## 8. Terrestrial Tests of the GR and RND Predictions

#### 8.1. Testing the One-Way Speed of Light Predictions

#### 8.2. Testing the Relativistic Time Dilation

## 9. The Metric of a Field from Several Sources in Whitehead’s and RND Models

## 10. Discussion

- Extend $RND$ to the field of a rotating, axially-symmetric massive object (similarly to the Kerr approach)
- Explore the implications of the metric (54) of a gravitational field of a moving source
- Compute the $RND$ metric of a binary and compare with the observational data
- Find the $RND$ metric for a field generated by several sources.

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The difference between $RND$ and $GR$ redshift predictions due to time dilation for the star SO-2.

**Figure 3.**Experiment testing $RND$ one-way speed of light predictions: (

**a**) the beam from A propagates toward the Earth and interferes with the beam from B, (

**b**) the same system is rotated ${180}^{\circ}$ and the beam from A propagates upward and interferes with the beam from B.

**Figure 4.**Experimental setup to test relativistic time dilation due to the velocity of the source in Earth’s gravitation field.

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**MDPI and ACS Style**

Friedman, Y.
Relativistic Gravitation Based on Symmetry. *Symmetry* **2020**, *12*, 183.
https://doi.org/10.3390/sym12010183

**AMA Style**

Friedman Y.
Relativistic Gravitation Based on Symmetry. *Symmetry*. 2020; 12(1):183.
https://doi.org/10.3390/sym12010183

**Chicago/Turabian Style**

Friedman, Yaakov.
2020. "Relativistic Gravitation Based on Symmetry" *Symmetry* 12, no. 1: 183.
https://doi.org/10.3390/sym12010183