Transition of EMRIs through resonance: Corrections to higher order in the on-resonance flux modification
View / Open Files
Publication Date
2017-11Journal Title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN
0022-2488
Publisher
AIP
Volume
58
Issue
11
Number
ARTN 112501
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Mihaylov, D., & Gair, J. R. (2017). Transition of EMRIs through resonance: Corrections to higher order in the on-resonance flux modification. JOURNAL OF MATHEMATICAL PHYSICS, 58 (11. ARTN 112501)https://doi.org/10.1063/1.5006336
Abstract
Extreme-mass-ratio inspirals (\textsc{emri}s) are candidate events for gravitational wave detection in the millihertz band (by detectors like \textsc{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 timescales approach implemented by Flanagan and Hinderer. In both cases, the exact treatment depends on the modelling of the gravitational self-force, which is currently not available. We extend the results in 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.
Sponsorship
STFC (1494582)
Identifiers
External DOI: https://doi.org/10.1063/1.5006336
This record's URL: https://www.repository.cam.ac.uk/handle/1810/271704
Rights
Licence:
http://www.rioxx.net/licenses/all-rights-reserved