Black-hole horizons as probes of black-hole dynamics. I. Post-merger recoil in head-on collisions.

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging problem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black-hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [L. Rezzolla, R.P. Macedo, and J.L. Jaramillo, Phys. Rev. Lett. 104, 221101 (2010).] with Robinson-Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualitative aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a "slowness parameter" and how this can be computed from the local properties of the horizon. In a companion paper [J. L. Jaramillo, R. P. Macedo, P. Moesta, and L. Rezzolla, following article, Phys. Rev. D 85, 084031 (2012).] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons. [ABSTRACT FROM AUTHOR]