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A brief overview is presented of a new Caltech/Cornell research program thatis exploring the nonlinear dynamics of curved spacetime in binary black holecollisions and mergers, and of an initial project in this program aimed atelucidating the flow of linear momentum in black-hole binaries (BBHs). The"gauge-dependence" (arbitrariness) in the localization of linear momentum inBBHs is discussed, along with the hope that the qualitative behavior of linearmomentum will be gauge-independent. Harmonic coordinates are suggested as apossibly preferred foundation for fixing the gauge associated with linearmomentum. For a BBH or other compact binary, the Landau-Lifshitz formalism isused to define the momenta of the binary's individual bodies in terms ofintegrals over the bodies' surfaces or interiors, and define the momentum ofthe gravitational field (spacetime curvature) outside the bodies as a volumeintegral over the field's momentum density. These definitions will be used insubsequent papers that explore the internal nonlinear dynamics of BBHs vianumerical relativity. This formalism is then used, in the 1.5PN approximation,to explore momentum flow between a binary's bodies and its gravitational fieldduring the binary's orbital inspiral. Special attention is paid to momentumflow and conservation associated with synchronous spin-induced bobbing of theblack holes, in the so-called "extreme-kick configuration" (where two identicalblack holes have their spins lying in their orbital plane and antialigned).

Momentum Flow in Black Hole Binaries: I. Post-Newtonian Analysis of the Inspiral and Spin-Induced Bobbing