Gravitational-Wave Extraction from Neutron Stars Oscillations: comparing linear and nonlinear techniques

The main aim of this study is the comparison of gravitational waveforms obtained from numerical simulations which employ different numerical evolution approaches and different wave-extraction techniques. For this purpose, we evolve an oscillating, nonrotating, polytropic neutron-star model with two different approaches: a full nonlinear relativistic simulation (in three dimensions) and a linear simulation based on perturbation theory. The extraction of the gravitational-wave signal is performed via three methods: the gauge-invariant curvature-perturbation theory based on the Newman-Penrose scalar c4; the gauge-invariant Regge-Wheeler-Zerilli-Moncrief metric-perturbation theory of a Schwarzschild space-time; some generalization of the quadrupole emission formula.