Deconfinement transition in rotating compact stars

Using the formalism of general relativity for axially symmetric gravitation al fields and their sources - rotating compact stars - a perturbation theor y with respect to angular velocity is developed and physical quantities suc h as mass, shape, momentum of inertia and total energy of the star are defi ned. The change of the internal structure of the star due to rotation has b een investigated and the different contributions to the moment of inertia h ave been evaluated separately. Numerical solutions have been performed usin g a two-flavor model equation of state describing the deconfinement phase t ransition as constrained by the conservation of total baryon number and ele ctric charge. During the spin down evolution of the rotating neutron star, below critical values of angular velocity a quark matter core can appear wh ich might be detected as a characteristic signal in the pulsar timing. With in the spin-down scenario due to magnetic dipole radiation it is shown that the deviation of the braking index from n = 3 could signal not only the oc currence but also the size of a quark core in the pulsar. A new scenario is proposed where, due to mass accretion onto the rapidly rotating compact st ar, a spin-down to spin-up transition might signal a deconfinement transiti on in its interior.