  The possibility of observationally discriminating between various types of
neutron stars, described by different equations of state of the nuclear matter,
as well as differentiating neutron stars from other types of exotic objects,
like, for example, quark stars, is one of the fundamental problems in
contemporary astrophysics. We consider and investigate carefully the
possibility that different types of rapidly rotating neutron stars, as well as
other type of compact general relativistic objects, can be differentiated from
the study of the emission properties of the accretion disks around them. We
obtain the energy flux, the temperature distribution and the emission spectrum
from the accretion disks around several classes of rapidly rotating neutron
stars, described by different equations of state of the neutron matter, and for
quark stars, described by the MIT bag model equation of state and in the CFL
(Color-Flavor-Locked) phase, respectively. Particular signatures appear in the
electromagnetic spectrum, thus leading to the possibility of directly testing
the equation of state of the dense matter by using astrophysical observations
of the emission spectra from accretion disks.
