Some Astrophysical Aspects of a Schwarzschild Geometry Equipped with a Minimal Measurable Length

By considering a deformation of the Schwarzschild metric in the presence of a minimal measurable length which still respects the equivalence principle, we study corrections to the standard general relativistic predictions for some astrophysical phenomena such as stability of circular orbits of black hole accretion disks, redshift of black hole accretion disks, gravitational tidal forces and the geodetic drift rate. We use the \emph{Gravity Probe B} data to see robustness of our results. Our analysis shows also that the relevant deformation parameter $\varepsilon$ which has a geometric origin, plays the same role as the charge to mass ratio, $\frac{e}{m}$ in the Reissner-Nordstr\"{o}m metric.