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Diagnostics for Numerical Simulations

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The Black Hole-Neutron Star Binary Merger in Full General Relativity

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

The purpose of this study is to analyze gravitational waves and merger remnants, and clarify their dependence on the NS EOS. In this chapter, we describe methods to extract gravitational waves from numerically computed spacetimes within a finite domain, and to obtain values of physical quantities associated with the remnant disk and BH.

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Notes

  1. 1.

    In general relativity, the Ricci tensor has the same information as that of the energy-momentum tensor.

  2. 2.

    The signature of the Weyl scalar is not universal. Some authors use the opposite signature, and then it is compensated by an additional minus sign for the relation between \(\varPsi _4\) and gravitational waves.

  3. 3.

    The Gram-Schmidt orthogonalization is not performed in SACRA. It is justified because the orthogonality is satisfied at the limit of the infinite radius, where the weak field limit is achieved.

  4. 4.

    We also performed this direct time integration in [16, 17], and present refined results computed by the fixed-frequency integration method, with which the results changes only very slightly for nonspinning BH–NS binaries.

  5. 5.

    To reduce systematic errors associated with this issue, extrapolation of \(\varPsi _4 (r)\) should be performed assuming some functional form, e.g., \(\varPsi _4 (r) = \varPsi _4 ( r \rightarrow \infty ) + \sum _{n>1} \varPsi _{4,n} r^{-n}\).

  6. 6.

    It is noted that the spectrum at high frequency for the Taylor-T4 formula depends on the location where time-domain gravitational waves are truncated. It does not affect the fitting procedure described in Chaps. 6 and 7 as far as we truncate the waveform before \(X\) and the amplitude become too large.

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Authors and Affiliations

  1. KEK, Cosmophysics Group, Institute of Particle and Nuclear Studies, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Koutarou Kyutoku

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Kyutoku, K. (2013). Diagnostics for Numerical Simulations. In: The Black Hole-Neutron Star Binary Merger in Full General Relativity. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54201-8_5

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