Effective geometry of a white dwarf

The ‘‘effective geometry’’ formalism is used to study the perturbations of a white dwarf described as aself-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type.The quantum nature of the system causes an absence of homological properties, manifested instead bypolytropic stars, and requires a parametric study of the solutions both at the numerical and analytical level.We have explicitly derived a compact analytical parametric approximate solution of Pade´ type, whichgives density curves and stellar radii in good accordance with already existing numerical results. Aftervalidation of this new type of approximate solutions, we use them to construct the effective acousticmetric governing general perturbations following Chebsch’s formalism. Even in this quantum case, thestellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in paststudies on nonquantum self-gravitating polytropic stars. The equations of the theory are finally numericallyintegrated in the simpler case of irrotational spherical pulsating perturbations, including the effect ofbackreaction, in order to have a dynamical picture of the process occurring in the acoustic metric.