A possible quantum probability increase of the cylindrical gravitational field

As known, the cylindrical gravitational field (wave) have been canonically quantized and its wave function, as the quantum one, interpreted in probability terms. We show in this work, using quantum Zeno methods, that this probability may be substantially increased and even approach unity. For that we first show, in detailed manner, that the cylindrical gravitational field may be discussed in the commutation number representation. We also discuss this field in the transverse-traceless (TT) gauge and calculate the related trapped surface.