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arXiv · 0711.2545

A spectral collocation approximation for the radial-infall of a compact object into a Schwarzschild black hole

Jae-Hun Jung·Gaurav Khanna·Ian Nagle
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Abstract

The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the point particle appear in the equation in the form of the Dirac $δ$-function and its derivative. For the approximation of singular source terms, we use the direct derivative projection method without any regularization. The gravitational waveforms are evaluated as a function of time. We compare the results of the spectral collocation method with those of the explicit second-order central-difference method. The numerical results show that the spectral collocation approximation with the direct projection method is accurate and converges rapidly when compared with the finite-difference method.

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Jae-Hun Jung, Gaurav Khanna, Ian Nagle. 2009-07-02. A spectral collocation approximation for the radial-infall of a compact object into a Schwarzschild black hole. https://doi.org/10.1142/s012918310901476x

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