Tidal effects based on a GUP-induced effective metric

Abstract

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