Gravitational Radiation from Binaries: A Pedagogical Introduction. (arXiv:1908.04410v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Jafari_A/0/1/0/all/0/1">Amir Jafari</a>

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 of mass $m$ around a

massive black hole of mass $Mgg m$. 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 $mll M$ 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 following Ori & Thorne (2000). We also briefly discuss the main

results of the extension of this model to 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.

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 of mass $m$ around a

massive black hole of mass $Mgg m$. 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 $mll M$ 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 following Ori & Thorne (2000). We also briefly discuss the main

results of the extension of this model to 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.

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