Observational Tests Capable of Validating a Dark Matter Explanation Without Exotic Matter

Observing S301 will make it possible to measure the angular momentum of SgrA*. General Relativity (GR), predicts nodal precession of $\Delta \Omega_{LT} \approx 10^{-3} rad/rev$. There exists a strong-field gravitomagnetic-type theory that explains dark matter (DM) through gravitational fields (without exotic matter) generating angular momenta greater than those predicted by GR. This DM explanation comes from linearized general relativity (GRL). We propose applying such fields to the supermassive black hole (SBH) SgrA*, a step that slightly extends the theory's explanatory framework for DM. However, it is quite plausible that SBH also harbor such fields, thereby generating such angular momenta. First, we define observationally derived parameter values for SgrA*, S2, and S301. We verify that these values are consistent with the currently expected and observed precession rates for S2 and S301. Second, we employ GRL to recover the already known expression for the black hole's angular momentum, allowing for an interpretation of this angular momentum within the GRL framework. Third, we calculate the potential precession effects induced by this DM solution. We demonstrate that, for S2, these precessions are too weak to be measured, in agreement with observation. But conversely, we demonstrate that, for S301, this DM solution could yield precession rates up to seven times higher than those expected from GR, $\Delta \Omega_{LT} \approx 7 \times 10^{-3} rad/rev$. Fourth, we propose a calculation of these GRL fields by initiating an elementary quantum theory of gravity. By this way, we also demonstrate that any measurement showing greater precession for S301 would not necessarily invalidate GR, as this DM solution is fully compatible with it; rather, it would confirm the existence of new gravitational fields driving the Lense-Thirring effect and would provide initial proof of the validity of this DM solution. Such new fields would constitute the first evidence for the necessity of a quantum theory of gravity, the fundamental elements of which are proposed in this article.