  After picking out what may seem more realistic minimal gravitational
deformation of quantum mechanics, we study its back reaction on gravity. The
large distance behaviour of Newtonian potential coincides with the result
obtained by using of effective field theory approach to general relativity (the
correction proves to be of repulsive nature). The short distance corrections
result in Planck mass black hole remnants with zero temperature. The
deformation of position-momentum uncertainty relations leads to the
superluminal motion that can be avoided by making similar deformation of
time-energy uncertainty relation. Such deformation also avoids UV divergences
in QFT.
