The regular motions of the Sun, the Moon and the planets can also be observed on an enormously different scale in the revolutions of binary star systems and the radio pulses from rotating neutron stars. In the last decades, less ordered and much more violent celestial phenomena have been discovered. Extraordinary, high-energy X-ray bursts come from binary star systems where one of the stars is a dense neutron star. Matter, mostly hydrogen, is detached from the normal companion star due to the powerful gravitational field of the neutron star; when this matter falls on the neutron star, most of its gravitational potential energy is released in the form of high-frequency emissions. When hydrogen reaches the surface of the star, it forms heavier elements, and nuclear fusion causes impressive thermonuclear fulgurations that can be seen from Earth as important X-ray bursts. Given the huge gravitational fields of these objects, this thesis seeks to find alternative explanations to these phenomena, and to analyze the possibility of detecting General Relativity effects. Simple models are analyzed, but the possibility is left open for future developments that may extend our knowledge.