No, a piece of paper cannot generate gravitational waves. Gravitational waves are ripples in the fabric of spacetime caused by the acceleration or movement of massive objects with significant energy. These waves are a consequence of Einstein's theory of general relativity.
Gravitational waves are produced by astrophysical events such as the collision of black holes, the explosion of supernovae, or the merging of neutron stars. These events involve extreme conditions of mass and energy, causing the surrounding spacetime to be distorted and sending out gravitational waves that propagate through the universe.
A piece of paper, on the other hand, does not possess the necessary mass, energy, or acceleration to generate gravitational waves of any noticeable magnitude. Gravitational waves require enormous amounts of mass and energy concentrated in a small region to create the disturbances in spacetime that are detectable.
In summary, gravitational waves arise from the motion of massive objects in extreme conditions, and a simple piece of paper does not meet the criteria to generate such waves.