Some of these discrepancies could corroborate the previous mentioned solution of dark matter (and then by the same time could be in agreement with general relativity). We will see that unexpected discrepancies are possible due to this gravitic field. That will allow testing the general relativity in extreme conditions. The goal of our study is to predict what could be the effect of the gravitic field at the center of our galaxy (SgrA*) on the measure of the gravitational redshift of the star SO-2 which will be soon very close to SgrA*. Even if the gravitic field of the galaxies’ center can’t explain the dark matter at the ends of the galaxies, it could be locally an important component of the dynamic of the object near the center (perhaps of the same order of the gravity field). In particular the center of galaxies could be a first example of such a phenomenon. More generally, this solution implies that large structures generate greater gravitic field (and then Lense-Thirring effect) than expected. This explanation leads to the assumption that we are embedded in a relatively uniform gravitic field generated by larger structures than galaxies (likely the clusters). In, a solution is proposed to explain the dark matter, compliant with general relativity and without exotic matter. Several experiments have validated this effect for the Earth gravitic field, NASA’s LAGEOS satellites or Gravity Probe B. This new gravitic field can be measured by its effect, known as Lense-Thirring effect. These both components give what is called the gravitomagnetism, obtained from the linearization of the general relativity. In addition to the gravity field, there is a gravitic field just like the magnetic field in electromagnetism. General relativity implies the existence of two gravitational components. And to end, if the discrepancy is larger, it will be more difficult to explain it in the frame of the general relativity (even in the frame of the explanation of dark matter as the effect of the term of gravitic field). In the three previous cases, this discrepancy will be a measure of the gravitic field of SMBH and would be an important clue that would indirectly corroborate the explanation of the dark matter as the effect of the term of gravitic field. The calculation of the mass will have to be revised. It will mean that the effect of the gravitic field at the Galaxy center is greater than expected and even greater than the effect of the gravity field. If a discrepancy is measured of around ZH~10-3 this discrepancy could always be explained in agreement with general relativity. Furthermore the calculation of the mass could have to be revised. It will mean that the effect of the gravitic field at the Galaxy center is greater than expected and can even be of the same order of magnitude than the effect of the gravity field. With a measure of around ZH~10-4, this discrepancy could always be explained in agreement with general relativity. If a discrepancy is measured of around ZH~10-5, the gravitic field at the Galaxy center will be greater than expected but always inferior to the effect of the gravity field. If the discrepancy measured on the gravitational redshift of SO-2 is ZH~10-5, it will mean that the gravitic field at the center of the Galaxy is too weak to be measured and, as expected, that the gravity field dominates. The value of the gravitic field of SMBH is not known but depending on its value, four cases (in agreement with general relativity) can be obtained. In the current paper, we study the component of the SO-2’s gravitational redshift due to the gravitic field of the galactic center (ZH) compared to the expected gravitational redshift due to the gravity field (ZG~3×10-4). But despite this, it seems possible that this gravitic field is in general underestimated. In this theoretical frame, the gravitic field of the galaxies cannot explain the dark matter at their ends. In the dark matter is explained by the second component (gravitic field) of the general relativity generated by the clusters. It will allow measuring relativistic effects. The star SO-2 at the galactic center will be soon at its closest distance to the supermassive black hole (SMBH).
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