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

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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