Higher-order corrections to the laws of motion and precession for black holes and other bodies

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Abstract
In a recent paper, Thorne and Hartle have derived laws of motion and precession for black holes and other bodies. Using two different methods, higher-order corrections to those laws are derived here: a time change of the body’s mass-energy due to coupling of the time derivatives of the body’s quadrupole moments to the external curvature; a force due to coupling of the time derivatives of the body’s quadrupole moments to the external curvature and coupling of the body’s quadrupole moments to the gradient of the external curvature; and a torque due to coupling of the body’s octopole moments to the gradient of the external curvature.

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