  After a critical overview of the Generalized Uncertainty Principle (GUP)
applied to compact objects, we propose a texture of Heisenberg uncertainty
principle in curved spacetimes (CHUP). CHUP allows to write down physically
motivated STUR (spacetime uncertainty relations) in a generic background for a
non commutative spacetime in terms of tetrad variables. In order to study
possible quantum effects for compact astrophysical objects as white dwarf,
neutron stars and black holes, an expression for quantum fluctuations is
outlined. As a result, contrary to GUP-based claims, we found no evidence for
quantum effects concerning equilibrium equation and critical mass $M_c$ for
white dwarf and neutron stars. Conversely, our expression for CHUP confirms
that general relativistic effects strongly reduce the Oppenheimer-Volkoff
Newtonian limit for very compact astrophysical objects as neutron stars. In
particular, we found that for a degenerate relativistic Fermi gas, the maximum
mass decreases for increasing compactness of the star with a minimum critical
mass $M_c\simeq 0.59 M_{\odot}$ at the Buchdahl limit. Finally, we study
possible non commutative effects near the event horizon of a black hole.
