Tidal effects based on GUP-induced effective metric

Abstract

In this paper, we study tidal forces in the Schwarzschild black hole whose metric includes explicitly a generalized uncertainty principle (GUP) effect. We also investigate interesting features of the geodesic equations and tidal effects dependent on the GUP parameter $\hat{I}\pm$ related to a minimum length. Then, by solving geodesic deviation equations explicitly with appropriate boundary conditions, we show that $\hat{I}\pm$ in the effective metric affects both the radial and angular components of the geodesic equation, particularly near the singularities.

13 pages, 9 figures, version to appear in Communications in Theoretical Physics