ON THE NONRADIAL OSCILLATIONS OF RELATIVISTIC STARS - A RELATIVISTIC COWLING APPROXIMATION

The non-radial oscillations of a general-relativistic incompressible fluid sphere are considered as a means of introducing a new (and very simple) Cowling approximation, in which the space-time metric is not perturbed at all. An f-mode spectrum is thus derived, reasonably accurate for l greater than or equal to 7, which shows how these frequencies depend upon the density and the Schwarzschild parameter S = 2M/R. Previous work by Detweiler has indicated that the quadrupole frequency is determined by the density alone, for values of S in the range which characterizes neutron stars; taken together, these results suggest an observational scheme by which an empirical mass-radius relation for neutron stars might be determined, and a firm upper limit on their masses established.