# Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves

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## Abstract

**:**

## 1. Introduction

## 2. General Relativity

**mass**density. We remind the reader that lowering and raising indices is done through the metric ${g}_{\mu \nu}$ and inverse metric ${g}^{\mu \nu}$, such that ${u}_{\mu}={g}_{\mu \nu}{u}^{\nu}$. The same metric serves to calculate s:

## 3. Linear Approximation of GR

**then**defines the quantity:

## 4. Beyond the Newtonian Approximation

## 5. Rotation Curves

#### 5.1. General Considerations

#### 5.2. M33 Density Profile

#### 5.3. M33 Rotation Curve

**current**estimation of the second derivative of mass; we make no claim about the past or future values of $\ddot{M}$, nor is there any claim in this section on the value of $\dot{M}$ at any time or the value of M in the past or the future. It is obvious that such questions involve an understanding of the mass exchange between the galaxy and the intergalactic medium, as described in Section 6.

## 6. A Dynamical Model

## 7. The Mass Formula

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The $\psi $ function of M33, the function converges to one for large distances as expected from Equation (44).

**Figure 5.**The $\chi $ function of M33; the function converges to one for large distances, as expected from Equation (42).

**Figure 6.**Rotation curve for M33. The observational points were supplied by Dr. Michal Wagman, a former PhD student at Ariel University, under my supervision, using [17]; the full line describes the complete rotation curve, which is the sum of the dotted line, describing the retardation contribution, and the dashed line, which is the Newtonian contribution.

**Figure 7.**An idealized cylindrical galaxy from different perspectives. (

**a**) From above; (

**b**) tilted edge perspective.

**Figure 9.**An initial density profile outside the galactic plane, in which ${\rho}_{0}={\rho}_{1}+{\rho}_{2},\frac{{\rho}_{2}}{{\rho}_{1}}=-0.2$ and ${z}_{i}=5$ (kpc) and $k=0.32\phantom{\rule{4pt}{0ex}}\left({\mathrm{kpc}}^{-1}\right)$.

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**MDPI and ACS Style**

Yahalom, A.
Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves. *Symmetry* **2020**, *12*, 1693.
https://doi.org/10.3390/sym12101693

**AMA Style**

Yahalom A.
Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves. *Symmetry*. 2020; 12(10):1693.
https://doi.org/10.3390/sym12101693

**Chicago/Turabian Style**

Yahalom, Asher.
2020. "Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves" *Symmetry* 12, no. 10: 1693.
https://doi.org/10.3390/sym12101693