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

## TL;DR

This paper explores how introducing a minimal measurable length into Schwarzschild geometry affects astrophysical phenomena, providing corrections to general relativity predictions and comparing them with Gravity Probe B data.

## Contribution

It presents a novel deformation of Schwarzschild metric incorporating a minimal length, analyzing its effects on astrophysical phenomena and relating the deformation parameter to charge-to-mass ratio.

## Key findings

- Deformation affects stability of black hole accretion disk orbits.
- Redshift predictions are modified by the minimal length.
- Gravity Probe B data constrains the deformation parameter.

## Abstract

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.