f-Mode instability in relativistic neutron stars.

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ℓ=m=4 mode) of the order of 10(3)-10(4)  s near the Kepler frequency Ω(K) while the instability is active above ∼0.92  Ω(K) and for temperatures ∼(10(9)-2×10(10))  K, characteristic of newborn neutron stars.