Deformation and maximum quadrupole moment for a single neutron star

The emergence of gravitational-wave astronomy has enabled us to unveil events that were previously concealed: compact binary coalescences. Neutron stars have been recognized as significant sources of gravitational radiation, thus triggering a timely exploration of their deformations. Through gravitational waves, scientists are presented with a unique opportunity to study the interiors of neutron stars and deepen the understanding of the equation of state of ultra-dense nuclear matter. In this article, reflects the necessary condition for the generation of gravitational radiation, namely the time-varying quadrupole moment, and calculate the ellipticity resulting from a neutron stars simplistic model. Subsequently, this article examine Ushomirskys research on the maximum quadrupole moment, in which this term does not show any explicit dependence on mass. Finally, the author makes a comparison between simplistic model and Ushomirsky, Haskell, gives a estimation on ellipticity and maximum quadrupole moment, expecting a potential improvement on the model would be incoporating dynamic terms.,such as accretion and star quakes.