Perturbation methods for the calculation of gravitational waves from slightly nonspherical spacetimes with applications to stellar core collapse

摘要

A method for the calculation of gravitational radiation from perturbations of spherically symmetric, realistic background stellar models is presented. The numerical background hydrodynamic code is based on a scheme developed by May and White, is fully relativistic, and can be used with any equation of state. Special emphasis will be placed on even-parity gravitational perturbations of the Einstein equations, but odd-parity perturbations will also be studied. For the odd-parity perturbations, based on the work of Moore, numerical results are presented for dust collapse to a black hole and for stellar collapse models designed to simulate a type II supernova. In this case, we find that odd-parity perturbations of such models are capable of radiating up to 10$sp{-7}$ stellar masses in gravitational radiation energy. For the even-parity perturbations, preliminary results are presented for dust collapse and for stellar collapse models with a polytropic equation of state. The polytropic models do not well represent current supernova models, but they do provide a basis for comparison of the even- and odd-parity perturbations under relativistic conditions in a collapsing star with a polytropic equation of state. For such polytropic stellar models we find that even-parity perturbations are capable of radiating an order of magnitude more in gravitational wave energy than corresponding odd-parity perturbations.