  Based on string theory, loop quantum gravity, black hole physics, and other
theories of quantum gravity, physicists have proposed generalized uncertainty
principle (GUP) modifications. In this work, within the framework of
GUP-gravity theory, we have successfully derived an exact solution to
Einstein$'$s field equation, discuss the possibility of using EHT to test GUP
and how GUP changes the weak cosmic censorship conjecture for black hole. We
analyze two different ways of constructing GUP rotating black holes (Model I
and Model II). Model I takes into account the modification of mass by GUP, i.e.
the change of mass by quantization of space, and the resulting GUP-rotating
black hole metric (18) is similar in form to Kerr black hole. Model II takes
into account the modification of the rotating black hole when GUP is an
external field, where GUP acts like an electric charge, and the resulting
GUP-rotating black hole metric (19) is similar in form to Kerr-Newman black
hole. By analyzing the shadow shape of the GUP rotating black hole, we have
discovered intriguing characteristics regarding the impact of first-order and
second-order momentum correction coefficients on the black hole's shadow shape.
These findings will be instrumental in future GUP testing using EHT.
Additionally, by incident test particle and scalar field with a rotating
GUP-black hole, the weak cosmic censorship conjecture is not violated in either
extreme black holes or near-extreme black hole.
