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A Spectral Collocation Approximation For The Radial-Infall Of A Compact Object Into A Schwarzschild Black Hole

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jae-Hun Jung & Gaurav Khanna & Ian Nagle, 2009. "A Spectral Collocation Approximation For The Radial-Infall Of A Compact Object Into A Schwarzschild Black Hole," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(11), pages 1827-1848.
    • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:11:n:s012918310901476x
    DOI: 10.1142/S012918310901476X
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