Quark-hadron phase transition in neutron stars

In the first part of this paper we introduce a suitable formulation of Athe hydrodynamical description of compact stars in a curved space-time Amanifold using the tetrad formalism. In the second part of the paper Awe review new developments concerning the possibility of quark Adeconfinement in neutron stars. Contrary to earlier claims, it is Ashown that "neutron" stars may very well contain quark matter in their Acores, which may register itself in an observable signal-an anomaly in Athe braking index of pulsars.