Radiation from collapsing relativistic stars. I - Linearized odd-parity radiation

Electromagnetic and gravitational radiation due to odd-parity sources in a collapsing Oppenheimer-Snyder (1939) background is analyzed. The sources and the fields they produce are treated as linearized perturbations, using gauge-invariant quantities. The perturbations are found to obey simple hyperbolic differential equations; numerical solutions to these wave equations are presented for the waveforms, energies, and spectra of the emitted radiation. The results show that: (1) the radiation peculiar to the late stages of collapse is rather independent of the internal dynamics of the collapsing star; (2) the nature of this radiation is governed by the background Schwarzschild spacetime surrounding the collapsing star; (3) the behavior of the perturbations at very late times conforms to theoretical predictions concerning 'power-law tails'; and (4) quasi-normal ringing dominates the emitted radiation. The excitation mechanism for the quasi-normal modes is considered.