In this article, we adopt the following notations:

– the spacetime metric, | |

– the three metric on a three dimensional hypersurface , | |

– the timelike unit hypersurface normal, | |

– the extrinsic curvature on , | |

– the trace of the extrinsic curvature, | |

– the lapse function, | |

– the shift vector, | |

– the determinant of , | |

– the determinant of ; , | |

– the covariant derivative associated with , | |

– the covariant derivative associated with , | |

– the stress energy momentum tensor, | |

– the baryon rest-mass density, | |

– the specific internal energy of the fluid, | |

– the pressure of the fluid, | |

– the specific enthalpy of the fluid, | |

– the polytropic constant, | |

– the adiabatic index, | |

– the four velocity of the fluid, | |

and | – the gravitational masses of NS and BH in isolation, |

– the baryon rest mass of NS, | |

– the total mass at infinite separation, | |

– the non-dimensional spin of BH, | |

– the spin angular momentum of BH, | |

– the compactness of NS in isolation, | |

– the circumferential radius of spherical NS, | |

– the orbital angular velocity, | |

– the frequency of gravitational waves, | |

– the wavelength of gravitational waves. |

Latin and Greek indices denote spatial and spacetime components, respectively. denotes the coordinate time. In Section 2 and the Appendix A, the geometrical units of are used, whereas in other sections, and are recovered.

Living Rev. Relativity 14, (2011), 6
http://www.livingreviews.org/lrr-2011-6 |
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