Relativistic effects explain the observations evidencing the existence of Dark Matter around galaxies and galaxy clusters. When energy passes closer to galaxies it “slows down” due to gravitational time dilations. This decrease in speed compared to the speed that energy has when travelling farther away from galaxies cannot be perceived by observers within the frames of reference closer to the center of galaxies. Ultimately the accumulative effect is a substantial increase in energy density when seen from a frame of reference far from the center of galaxies and that increased energy density is imperceptible for an observer within the galaxy’s inner frames of reference.  The higher concentration of travelling energy around galaxies in effect has a relativistic equivalent mass that is creating extra gravitational distortion in space-time. This extra gravity is in fact the unaccounted gravity attributed to Dark Matter.


From the beginning of existence energy’s own movement created and still is creating new fabric of space-time. Every unit of volume of space in the universe is being crossed from all possible spatial directions by traveling energy   in the form of neutrinos, electromagnetic  waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of waves and particles yet to be discovered. The lines traced by each quantum of energy (world lines) can be seen as fibers that intersect themselves in a way that they weave space-time fabric. The “fibers” of this Energy Felt get denser around galaxies and galaxy clusters. Any field studied by quantum mechanics is a manifestation of the Energy Felt in a particular range of frequencies of the energy spectrum.

Using a thought experiment this document proves that traveling energy (neutrinos, electromagnetic  waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of energy and particles yet to be discovered) is getting relativistically accumulated around galaxies and galaxy clusters.

Explaining “Observed” Dark Matter using General Relativity

Let’s imagine two identical laser pointers, Pa and Pb. Pa is going to be pointing in that way that its emitted photons (A) will pass parallel to Andromeda Galaxy galactic plane, at a minimum distance of one radius of Andromeda (Ra). Similarly Pb is pointing perfectly parallel to Pa in a way that its emitted photons (B) will pass at a minimum distance of 10 times Andromeda Radius (10Ra), for simplicity let’s omit gravitational lensing distortion. We set two light detectors, Da and Db at the other side of the galaxy in order to catch the photons emitted by Pa and Pb respectively.


General Relativity tells us that there is a different gravitational time dilation on the two different frames of reference; the frame of reference at Ra distance to the galactic plane and the frame of reference at 10Ra. For a rough calculation let’s use  Andromeda’s mass including Dark Matter and calculate time for the two frames of reference at the moment when each photon gets to its closest point to the galaxy’s center.


There is a gravitational time dilation ratio (Ta/Tb) of 100.2% at the instant when the photons are closest to the center of the galaxy.

If time dilation for photons emitted by Pa were to remain constant along the 200.000 light years across the galaxy the photons hitting Da would take 400 years more than the photons hitting Db as measured by a clock on Db , but this is not the case. The gravitational field varies through the photons voyage.figure-2For all photons traveling on a plane parallel to the galaxy disk at Ra distance the ratio (Ta/Tb) decreases when the photons are farther away from the center of the galaxy depending on the actual mass-energy distribution of the galaxy. This is better visualized  by a tridimensional distribution curved surface.figure-3Generalizing the time dilation ratio for two different radii (r1,r2) we can have:

Let’s use r2 as a fixed radius                          r2  =  Ȓ

And let’s use r1 as our only variable,           r1  =  requation-3To calculate an average of time dilation ratio (Tμ ) we will integrate spherical surfaces (onion layers) multiplied by time dilation ratio while the radius varies and our product will be divided by the volume for Ȓ. Our approximation will put 60% of Andromeda’s mass including Dark Matter as if it were inside an hypothetical  sphere with radius (ř) and stellar density (Ds); our integral will be calculated starting at a stellar density radius (ř) all the way to orbital radius (Ȓ)equation-45

The average time of relativistic accumulation for a sphere with r=Ȓ  is:equation-6The total relativistically accumulated mass-energy (Mω) in a sphere with  r= Ȓ using of the one hundredth of the value for Vacuum Energy Density as Traveling Energy Density per Second or roughly 1/3 of upper limit density of neutrinos in the universe (3.3*10^-28 kg/m^3) per second:equation-7We will use stellar density radius (ř) as our lower limit for integration:equation-8

Discussion and Conclusion

 A star orbiting at Ȓ distance from the center of the galaxy will “feel” the combined effect of the gravity generated by the baryonic mass and the relativistically accumulated mass-energy inside that sphere. All the mass (baryonic and relativistically accumulated mass-energy) located outside that sphere is also “felt” but it’s gravitational net effect cancels out. This is similar to calculations for an object falling through a hole towards the center of a planet where its acceleration only depends on the mass of a sphere with a radius equal to the object distance to the center of that planet.

This approximation demonstrates the mechanism for mass-energy relativistic accumulation around galaxies and more precise models should render results better matched with actual ‘Observed” Dark Matter measurements.

Furthermore, we do not have observations of the gravitational effects of Dark Matter taken outside of the Milky Way and time in our frame of reference is also dilated when compared to time at a point far away from the Milky Way. Our observations therefore should show differences with those of an observer outside our galaxy.

In the space between galaxies energy density gets higher than that of the surrounding space because of both galaxies’ gravity compounded effect. These structures connect galaxies and galaxy clusters together forming the Cosmic Web.

Dark Matter concentration ratio is different for different galaxies and galaxy clusters, not only because differences in mass distribution but also because galaxies have different masses. In addition, younger galaxies do have less Dark Matter in proportion to regular matter  since the mass-energy relativistic accumulation has a compounding effect over time: The higher the energy density ratio; the more mass-energy relativistic accumulation, the more mass-energy relativistic accumulation; the more gravity, the more gravity; the more mass-energy relativistic accumulation. Even though in the early universe energy density was higher, that density was more uniformly distributed. That means that the further away we look to younger galaxies, the less Dark Matter we should find. What causes the mass-energy relativistic accumulation is the difference in energy density close to the galaxies in comparison with that of the galaxies’ surrounding space.

It is this paper conclusion that there is no need for particularly special particles forming Dark Matter substance or even parallel universes’ escaped  gravity to account for the extra gravity existing around cosmic structures.  In a way, Dark Matter is just traveling energy and we need just a tiny fraction of the value of Vacuum Energy density per second or roughly 1/3 of upper limit density of neutrinos in the universe per second to make our model work. Einstein was right and his findings continue to enlighten our understanding of the universe.



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