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The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.
We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic E
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the m
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of separating the limi
We first give a way which satisfies the bidirectional derivation between the generalized uncertainty principle and the corrected entropy of black holes. By this way, the generalized uncertainty principle can be indirectly modified by some correction
We study Quantum Gravity effects in cosmology, and in particular that of the Generalized Uncertainty Principle on the Friedmann equations. We show that the Generalized Uncertainty Principle induces variations of the energy density and pressure in the