We describe the dynamical behavior of newborn pulsars modeled as homogeneous rotating spheroids. The dynamical evolution is triggered by the escape of trapped neutrinos, provided the initial equilibrium configuration. It is shown that for a given set
of values of the initial angular momentum a shape transition to a triaxial ellipsoid configuration occurs. Gravitational waves are then generated by the breaking of the axial symmetry, and some aspects of their observation are discussed. We found a narrow window for the initial values of the angular frequency and the eccentricity able to enable a dynamical shape transition, with the Kepler frequency of the rotating fluid determining the upper bound of the initial angular frequency and eccentricity. The loss of energy and angular momentum carried away by the gravitational wave is treated consistently with the solution of the equations of motion, which govern the dynamical evolution of the system. The transition in the shape of the core of the pulsar is weakly dependent on the time scale of the neutrino escape.
We present a simplified description of a rotating neutron star emitting gravitational waves. We describe the system by an uniformly rotating triaxial homogeneous ellipsoid to catch the main aspects of the evolution. We construct an effective Lagrangi
an model, in which the kinetic energy associated to the breath mode and rotation are explicitly determined. The rate of gravitational waves radiation is determined in the framework of the weak field limit approximation of Einstein equations. We then solve numerically the equations of motion for the nascent neutron star, incorporating the diffusion of neutrinos in the calculation.
