Extreme-mass-ratio inspirals are candidate events for gravitational wave detection in the millihertz band (by detectors like Laser Interferometer Space Antenna (lisa)). These events involve a stellar-mass black hole, or a similar compact object, descending in the gravitational field of a supermassive black hole, eventually merging with it. Properties of the inspiralling trajectory away from resonance are well known and have been studied extensively; however, little is known about the behaviour of these binary systems at resonance, when the radial and lateral frequencies of the orbit become commensurate. We describe the two existing models: the instantaneous frequency approach used by Gair, Bender, and Yunes and the standard two-time scale approach implemented by Flanagan and Hinderer. In both cases, the exact treatment depends on the modeling of the gravitational self-force, which is currently not available. We extend the results from the work of Gair, Bender, and Yunes to higher order in the on-resonance flux modification and argue that the instantaneous frequency approach is also a valid treatment of the resonance problem. The non-linear differential equations which arise in treating resonances are interesting from a mathematical view point. We present our algorithm for perturbative solutions and the results to third order in the infinitesimal parameter and discuss the scope of this approach.
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November 2017
Research Article|
November 13 2017
Transition of EMRIs through resonance: Corrections to higher order in the on-resonance flux modification
Deyan P. Mihaylov
;
Deyan P. Mihaylov
a)
1
Institute of Astronomy, University of Cambridge
, Madingley Road, Cambridge CB3 0HA, United Kingdom
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Jonathan R. Gair
Jonathan R. Gair
b)
1
Institute of Astronomy, University of Cambridge
, Madingley Road, Cambridge CB3 0HA, United Kingdom
2
School of Mathematics, University of Edinburgh
, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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J. Math. Phys. 58, 112501 (2017)
Article history
Received:
December 21 2016
Accepted:
September 22 2017
Citation
Deyan P. Mihaylov, Jonathan R. Gair; Transition of EMRIs through resonance: Corrections to higher order in the on-resonance flux modification. J. Math. Phys. 1 November 2017; 58 (11): 112501. https://doi.org/10.1063/1.5006336
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