Scientific Research

An Academic Publisher

The Gravitational Radiation Emitted by a System Consisting of a Point Particle in Close Orbit around a Schwarzschild Black Hole

**Author(s)**Leave a comment

We analytically model a relativistic problem consisting of a point-particle with mass m in close orbit around a stationary Schwarzschild black hole with mass M = 1 using the null-cone formalism when l = 2. We use the -function to model the matter density of the particle. To model the whole problem, we apply the second order differential equation obtained elsewhere for a dynamic thin matter shell around a Schwarzschild black hole. The only thing that changes on the equation is the quasi-normal mode parameter which now represent the orbital frequency of the particle. We compare our results with that of the standard 5.5 PN formalism and found that there is a direct proportionality factor that relates the two results, i.e. the two formalisms.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Kubeka, "The Gravitational Radiation Emitted by a System Consisting of a Point Particle in Close Orbit around a Schwarzschild Black Hole,"

*Journal of Modern Physics*, Vol. 3 No. 10, 2012, pp. 1503-1515. doi: 10.4236/jmp.2012.310186.

[1] | K. A. Postnov and L. R. Yungelson, “The Evolution of Compact Binaries Star Systems,” Living Reviews in Relativity, 9, 2006, p. 6. http://www.livingreviews.org/lrr-2006-6 |

[2] | S. Chandrasekhar, “Ellipsoidal Figures of Equilibrium,” Yale University Pres, New Heaven, 1969. |

[3] | L. G. Fishbone, “The Relativistic Roche Problem. I. Equilibrium Theory for a Body in Equatorial, Circular Orbit around a Kerr Black Hole,” Astrophysical Journal, Vol. 185, 1973, pp. 43-68. doi:10.1086/152395 |

[4] | M. Ishii, M. Shibata and Y. Mino, “Black Hole Tidal Problem in the Fermi Normal Coordinates,” Physical Review D, Vol. 71, No. 4, 2005, Article ID: 044017. doi:10.1103/PhysRevD.71.044017 |

[5] | D. Lai and A. G. Wiseman, “Innermost Stable Circular Orbit of Inspiraling Neutron-Star Binaries: Tidal Effects, Post-Newtonian Effects, and the Neutron-Star Equation of State,” Physical Review D, Vol. 54, No. 6, 1996, pp. 3958-3964. doi:10.1103/PhysRevD.54.3958 |

[6] | M. C. Miller, “Prompt Mergers of Neutron Stars with Black Holes,” Astrophysical Journal, Vol. 626, No. 1, 2005, p. L41. doi:10.1086/431583 |

[7] | B. Mashhoon, “On Tidal Phenomena in a Strong Gravitational Field,” Astrophysical Journal, Vol. 705, 1975, pp. 705-716. doi:10.1086/153560 |

[8] | B. Carter and J. P. Luminet, “Tidal Compression of a Star by a Large Black Hole,” Astronomy & Astrophysics, Vol. 121, 1983, pp. 97-113. |

[9] | B. Carter and J. P. Luminet, “Mechanics of the Affine Star Model,” Monthly Notices of the Royal Astronomical Society, Vol. 212, 1985, pp. 23-55. |

[10] | W. H. Lee, “Newtonian Hydrodynamics of the Coalescence of Black Holes with Neutron Stars—III. Irrotational Binaries with a Stiff Equation of State,” Monthly Notices of the Royal Astronomical Society, Vol. 318, No. 2, 2000, pp. 606-624. doi:10.1046/j.1365-8711.2000.03870.x |

[11] | W. H. Lee, “Newtonian Hydrodynamics of the Coalescence of Black Holes with Neutron Stars—IV. Irrotational Binaries with a Soft Equation of State,” Monthly Notices of the Royal Astronomical Society, Vol. 328, No. 2, 2001, pp. 583-600. doi:10.1046/j.1365-8711.2001.04898.x |

[12] | S. Kobayashi, P. Laguna, E. S. Phinney and P. Meszaros, “Gravitational Waves and X-Ray Signals from Stellar Disruption by a Massive Black Hole,” Astronomy & Astrophysics, Vol. 615, No. 2, 2004, p. 855. doi:10.1086/424684 |

[13] | S. Rosswog, R. Speith and G. A. Wynn, “Accretion Dynamics in Neutron Star—Black Hole Binaries,” Monthly Notices of the Royal Astronomical Society, Vol. 351, No. 4, 2004, pp. 1121-1133. doi:10.1111/j.1365-2966.2004.07865.x |

[14] | T. W. Baumgarte, M. L. Skoge and S. L. Shopiro, “Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation,” Physical Review D, Vol. 70, No. 6, 2004, Article ID: 064040. doi:10.1103/PhysRevD.70.064040 |

[15] | P. Grandclément, “Accurate and Realistic Initial Data for Black Hole-Neutron Star Binaries,” Physical Review D, Vol. 74, No. 12, 2006, Article ID: 124002. doi:10.1103/PhysRevD.74.124002 |

[16] | P. Grandclément, “Erratum: Accurate and Realistic Initial Data for Black Hole-Neutron Star Binaries,” Physical Review D, Vol. 74, 2007, Article ID: 129903(E). |

[17] | K. Taniguchi, T. W. Baumgarte, J. A. Faber and S. L. Shapiro, “Quasiequilibrium Black Hole-Neutron Star Binaries in General Relativity,” Physical Review D, Vol. 75, No. 8, 2007, Article ID: 084005. doi:10.1103/PhysRevD.75.084005 |

[18] | K. Taniguchi, T. W. Baumgarte, J. A. Faber and S. L. Shapiro, “Black Hole-Neutron Star Binaries in General Relativity: Effects of Neutron Star Spin,” Physical Review D, Vol. 72, No. 4, 2005, Article ID: 044008. doi:10.1103/PhysRevD.72.044008 |

[19] | K. Taniguchi, T. W. Baumgarte, J. A. Faber and S. L. Shapiro, Physical Review D, Vol. 74, 2006, Article ID: 041502(R). |

[20] | J. A. Faber, T. W. Baumgarte, S. L. Shapiro and K. Taniguchi, “General Relativistic Binary Merger Simulations and Short Gamma-Ray Bursts,” Astrophysical Journal, Vol. 641, No. 2, 2006, p. L93. doi:10.1086/504111 |

[21] | J. A. Faber, T. W. Baumgarte, S. L. Shapiro, K. Taniguchi and F. A. Rasio, “Dynamical Evolution of Black Hole-Neutron Star Binaries in General Relativity: Simulations of Tidal Disruption,” Physical Review D, Vol. 73, No. 2, 2006, Article ID: 024012. doi:10.1103/PhysRevD.73.024012 |

[22] | F. Loffler, L. Rezzollas and M. Ansorg, “Numerical Evolutions of a Black Hole-Neutron Star System in Full General Relativity: Head-On Collision,” Physical Review D, Vol. 74, No. 10, 2006, Article ID: 104018. doi:10.1103/PhysRevD.74.104018 |

[23] | M. Shibata and K. Uryū, “Merger of Black Hole-Neutron Star Binaries: Nonspinning Black Hole Case,” Physical Review D, Vol. 74, 2006, Article ID: 121503(R). |

[24] | M. Shibata and K. Uryū, “Merger of Black Hole-Neutron Star Binaries in Full General Relativity,” Classical and Quantum Gravity, Vol. 24, No. 12, 2007, p. S125. doi:10.1088/0264-9381/24/12/S09 |

[25] | C. F. Sopuerta, U. Sperhake and P. Laguna, “Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries,” Classical and Quantum Gravity, Vol. 23, No. 16, 2006, p. S579. doi:10.1088/0264-9381/23/16/S15 |

[26] | B. C. Barish and R. Weiss, “LIGO and the Detection of Gravitational Waves,” Physics Today, Vol. 52, No. 10, 1990, p. 44. doi:10.1063/1.882861 |

[27] | A. Coory, A. J. Farmer and N. Seto, “The Optical Identification of Close White Dwarf Binaries in the Laser Interferometer Space Antenna Era,” Astrophysical Journal Letters, Vol. 601, No. 1, 2004, p. L47. doi:10.1086/381780 |

[28] | L. Lehner, “Gravitational Radiation from Black Hole Spacetime,” Ph.D. Thesis, University of Pittsburg, Pittsburg, 1998. |

[29] | H. Bondi, M. J. G. van der Burg and A. W. K. Metzner, “Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems,” Proceedings of the Royal Society A, Vol. 269, No. 1336, 1962, pp. 21-52. doi:10.1098/rspa.1962.0161 |

[30] | R. K. Sachs, “Gravitational Waves in General Relativity. VIII. Waves in Asymptotically Flat Space-Time,” Proceedings of the Royal Society A, Vol. 270, 1962, pp. 103-126. |

[31] | N. T. Bishop, R. Gómez, L. Lehner, M. Maharaj and J. Winicour, “High-Powered Gravitational News,” Physical Review D, Vol. 56, No. 10, 1997, pp. 6298-6309. doi:10.1103/PhysRevD.56.6298 |

[32] | N. T. Bishop, “Linearized Solutions of the Einstein Equations within a Bondi-Sachs Framework, and Implications for Boundary Conditions in Numerical Simulations,” Classical and Quantum Gravity, Vol. 22, No. 12, 2005, p. 2393. doi:10.1088/0264-9381/22/12/006 |

[33] | N. T. Bishop and A. S. Kubeka, “Quasinormal Modes of a Schwarzschild White Hole,” Physical Review D, Vol. 80, No. 6, 2009, Article ID: 064011. doi:10.1103/PhysRevD.80.064011 |

[34] | E. Poisson, “Gravitational Radiation from a Particle in Circular Orbit around a Black Hole. I. Analytical Results for the Nonrotating Case,” Physical Review D, Vol. 47, No. 4, 1993, p. 1497. doi:10.1103/PhysRevD.47.1497 |

[35] | M. Sasaki and H. Tagoshi, “Analytic Black Hole Perturbation approach to Gravitational Radiation,” Living Reviews in Relativity, Vol. 6, 2003, p. 6. |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.