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Frequencies of non-axisymmetric f-modes in rapidly rotating polytropes in full general relativity

The computation of frequencies of non-axisymmetric f-modes in rapidly rotating stars in full general relativity is a long-standing problem that has not been solved, to date, without resorting to some approximation, such as the slow-rotation approximation or the Cowling approximation. We present the first computation of such frequencies in full general relativity and rapid rotation, without any such approximation. We achieve this by using long-term simulations of oscillating polytropic models with a nonlinear numerical code, where spacetime is evolved in the harmonic formulation. We compare our results to previous results for zero-frequency (neutral modes) that were obtained with a perturbative method, and comment on the relevance of our work to the gravitational-radiation-driven (CFS) secular instability of non-axisymmetric f-modes.

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