A SPECTRAL COLLOCATION APPROXIMATION FOR THE RADIAL-INFALL OF A COMPACT OBJECT INTO A SCHWARZSCHILD BLACK HOLE

Jae-Hun Jung (), Gaurav Khanna () and Ian Nagle
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Jae-Hun Jung: Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, USA
Gaurav Khanna: Department of Physics, University of Massachusetts at Dartmouth, North Dartmouth, MA 02747, USA
Ian Nagle: Department of Physics, University of Massachusetts at Dartmouth, North Dartmouth, MA 02747, USA

International Journal of Modern Physics C (IJMPC), 2009, vol. 20, issue 11, 1827-1848

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 proposed in Ref. 9 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.

Keywords: Zerilli equation; Chebyshev spectral collocation method; Schwarzschild black hole (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S012918310901476X

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