We discuss the properties of matter in the low temperature regime at density that may exist in the core of compact stars.
Assuming that in these conditions quarks are deconfined the attractive
color interaction determines the formation of Cooper pairs of quarks
and the resulting quark matter has properties analogous to standard
We show that under reasonable conditions a state were Cooper pairs
have non-zero total momentum is energetically favored and the
resulting non-homogeneous condensate is characterized by a crystal
Studying the elastic properties of such a state we find that it
behaves like a solid crystal with a very large shear modulus.
Our results raise the possibility that
(some) pulsar glitches may originate within the Crystalline Color
Superconductor core of Neutron stars.