| Neutron stars are small size objects (~10-20 Km) with a mass comparable to the one of our Sun (~1.4 solar masses). Their density and gravity is therefore immense: only black holes can be more compact and have stronger gravitational fields. However, neutron stars are the most extreme objects we can directly observe in the Universe. They are excellent laboratories to tests not only General and Special Relativity but also quantum mechanics and particle physics thanks to their huge densities well above the atomic nuclei densities. In this project I raise the question on the possibility of detecting accreting X-ray pulsars spinning at sub-millisecond periods. Such rapid rotating neutron stars are predicted by the standard accretion theory. However, in more than 40 years of X-ray astronomy, none of them has ever been discovered. I will explore new ideas to test the standard accretion theory in accreting X-ray pulsars and verify if there exist a mechanism that balances accretion torques and limits the spin period to be above the millisecond. I will also build a new code to automate and optimize pulse searches and perform the deepest and most extendend survery ever made, to search new accreting X-ray pulsars and verify the existence or the lack of sub-millisecond neutron star periods. The results of my project will have a huge impact in several fields of physics and astrophysics, allowing fundamental experiments of ultradense matter and gravitational waves, and a deeper knowledge of the accretion process in binary systems and new insights on the magnetic field evolution in such extreme systems. |