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arXiv 1908.04410gr-qcastro-ph.HE
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双星的引力辐射:教学导论

Gravitational Radiation from Binaries: A Pedagogical Introduction

Amir Jafari

摘要:

这篇短文是通过回顾极端质量比双星中的吸气-坍缩转变相来介绍引力辐射的。研究了质量为$m$的致密天体(CO)围绕质量为$M\gg m$的大质量黑洞的相对论运动.本文简要地评述了Kerr-Newman度规、椭圆轨道的有效势、Kerr时空中CO凝聚的引力辐射、轨道能量和角动量以及引力波频率和信噪比。主要的重点是从螺旋的过渡到暴跌的CO假设一个测试粒子的方法是合理的制度$m\ll M$没有呼吁微扰分析。有效势被用来获得的最内稳定的圆形轨道(ISCO)附近的绝热inspiral阶段突然结束,CO进入暴跌阶段的属性。对于过渡相,有效势展开的参数,如径向(坐标)距离的ISCO和偏离粒子的角动量从它的值在ISCO,以获得运动方程。将涡旋和转捩阶段的运动方程用数值方法连接起来,得到了圆/斜轨道和椭圆/斜轨道转捩阶段的引力波频率、波周数和信噪比(SN)。目前的方法来处理这个问题的局限性和不准确性进行了讨论。附录中还简要介绍了广义相对论的基本概念,特别是爱因斯坦场方程。

英文摘要:

This short note serves as an introduction to gravitational radiation through reviewing the inspiral-plunge transition phase in extreme mass ratio binaries. We study the relativistic motion of a compact object (CO) of mass $m$ around a massive black hole of mass $M\gg m$. The Kerr-Newman metric, effective potential for the general case of elliptical orbits, gravitational radiation, orbital energy and angular momentum of a coalescing CO in Kerr spacetime and gravitational wave frequency and signal to noise ratio are briefly reviewed. The main focus is on the transition from inspiral to plunge for a CO assuming that a test particle approach is plausible in the regime $m\ll M$ without appealing to a perturbative analysis. The effective potential is used to obtain the properties of the Innermost Stable Circular Orbit (ISCO) near which the adiabatic inspiral phase ends abruptly and the CO enters the plunge phase. For the transition phase, the effective potential is expanded in terms of parameters such as the radial (coordinate) distance from the ISCO and the deviation of particle's angular momentum from its value at the ISCO to obtain the equation of motion. The equations of motion, during the inspiral and transition phases, are joined numerically and the gravitational wave frequency, number of wave cycles and signal to noise ratio (SN) during the transition is obtained for circular/inclined as well as elliptical/inclined orbits. The limitations and inaccuracies of the current methods used to approach this problem is discussed. A short introduction to the fundamental concepts of General Relativity, in particular Einstein Field Equations is also provided in the Appendix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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