Gravitational waves from ultracompact stars: The optical geometry view of trapped modes

Abstract

Ultracompact stars - if they exist - have a unique signature: a discrete spectrum of slowly damped gravitational-wave quasinormal modes. It is known that this feature is due to a potential well present for stars with R < 3M. In this letter we show that the appearance of this well is essentially due to the non-Newtonian behaviour of the centrifugal potential: here we explain this behaviour adopting the optical geometry point of view. This insight leads us to an approximation, valid for highly compact stars, by which the real part of the spectrum is easily computed with good accuracy.