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Forced motion near black holes

Gair, Jonathan R. and Flanagan, Éanna É. and Drasco, Steve and Hinderer, Tanja and Babak, Stanislav (2011) Forced motion near black holes. Physical Review D, 83 (4). Art. No. 044037. ISSN 2470-0010.

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We present two methods for integrating forced geodesic equations in the Kerr spacetime. The methods can accommodate arbitrary forces. As a test case, we compute inspirals caused by a simple drag force, mimicking motion in the presence of gas.We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what others have observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would thus provide clear evidence that the inspiral was occurring in a nonvacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In the first method, the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a direct generalization of earlier work by Pound and Poisson [A. Pound and E. Poisson, Phys. Rev. D 77, 044013 (2008).] for planar forces in a Schwarzschild background.

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Hinderer, Tanja0000-0002-3394-6105
Additional Information:© 2011 American Physical Society. Received 22 December 2010; published 22 February 2011. The work was supported in part by NSF Grant Nos. PHY-0757735 and PHY-0457200 at Cornell and NSF Grant Nos. PHY-0653653 and PHY-0601459, CAREER Grant No. PHY-0956189, the David and Barbara Groce Start-up Fund, and the Sherman Fairchild Foundation at Caltech. J. G.’s work is supported by the Royal Society. S.B. and S. D. were supported in part by DFG Grant No. SFB/TR 7 Gravitational Wave Astronomy and by DLR (Deutsches Zentrum fur Luft- und Raumfahrt). E. F. is grateful for the hospitality of the Theoretical Astrophysics Including Relativity Group at Caltech and the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, as this paper was being completed.
Funding AgencyGrant Number
David and Barbara Groce startup fundUNSPECIFIED
Caltech Sherman Fairchild FoundationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG) GermanySFB/TR 7
Deutsches Zentrum fur Luft- und Raumfahrt (DLR)UNSPECIFIED
Issue or Number:4
Classification Code:PACS: 04.30.Db, 04.25.Nx
Record Number:CaltechAUTHORS:20110316-093514052
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Official Citation:Forced motion near black holes Jonathan R. Gair, Éanna É. Flanagan, Steve Drasco, Tanja Hinderer, and Stanislav Babak Published 22 February 2011 (27 pages) 044037
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22922
Deposited By: Ruth Sustaita
Deposited On:17 Mar 2011 18:26
Last Modified:09 Mar 2020 13:18

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