Thorne, Kip S. and Hartle, James B. (1985) Laws of motion and precession for black holes and other bodies. Physical Review D, 31 (8). pp. 18151837. ISSN 05562821. http://resolver.caltech.edu/CaltechAUTHORS:THOprd85

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Abstract
Laws of motion and precession are derived for a Kerr black hole or any other body which is far from all other sources of gravity ("isolated body") and has multipole moments that change slowly with time. Previous work by D’Eath and others has shown that to high accuracy the body moves along a geodesic of the surrounding spacetime geometry, and FermiWalker transports its angularmomentum vector. This paper derives the largest corrections to the geodesic law of motion and FermiWalker law of transport. These corrections are due to coupling of the body’s angular momentum and quadrupole moment to the Riemann curvature of the surrounding spacetime. The resulting laws of motion and precession are identical to those that have been derived previously, by many researchers, for test bodies with negligible selfgravity. However, the derivation given here is valid for any isolated body, regardless of the strength of its selfgravity. These laws of motion and precession can be converted into equations of motion and precession by combining them with an approximate solution to the Einstein field equations for the surrounding spacetime. As an example, the conversion is carried out for two gravitationally bound systems of bodies with sizes much less than their separations. The resulting equations of motion and precession are derived accurately through post1.5Newtonian order. For the special case of two Kerr black holes orbiting each other, these equations of motion and precession (which include couplings of the holes’ spins and quadrupole moments to spacetime curvature) reduce to equations previously derived by D’Eath. The precession due to coupling of a black hole’s quadrupole moment to surrounding curvature may be large enough, if the hole lives at the center of a very dense star cluster, for observational detection by its effects on extragalactic radio jets. Unless the hole rotates very slowly, this quadrupoleinduced precession is far larger than the spindown of the hole by tidal distortion ("horizon viscosity"). When the hole is in orbit around a massive companion, the quadrupoleinduced precession is far smaller than geodetic precession.
Item Type:  Article 

Additional Information:  ©1985 The American Physical Society. Received 9 July 1984. The authors are grateful to T. Damour for many useful discussions and several critical readings of the manuscript, to M.J. Rees for a stimulating conversation, and to the members of the Caltech Paradigm Society, especially X.H. Zhang, for helpful suggestions about the manuscript. This work was supported in part by the National Science Foundation under Grants Nos. AST8214126, PHY7727084, PHY8026043, and PHY8107384. 
Group:  TAPIR 
Record Number:  CaltechAUTHORS:THOprd85 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:THOprd85 
Alternative URL:  http://dx.doi.org/10.1103/PhysRevD.31.1815 
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ID Code:  9981 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  01 Apr 2008 
Last Modified:  26 Dec 2012 09:55 
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