Implication of geodesic equation in Generalized Uncertainty Principle framework

Understand

The generalized uncertainty principle (GUP) corrected modified relativistic particle model has been derived in curved space-time.

• From this modified model, the equation of motion (EM) has been constructed relativistically in terms of the affine parameter ($\lambda$) or proper time ($\tau$) and nonrelativistically in terms of coordinate time ($t$).
• In this context, the constraint analysis technique has been applied to get the EM.
• Interestingly, the EM obtained in both cases is the usual one.