Black-hole horizons as probes of black-hole dynamics II: geometrical insights

In a companion paper [1], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test screens. More specifically, dynamical horizons provide appropriate inner screens in a 3+1 setting and, in this context, we have shown that an effective-curvature vector measured at the common horizon produced in a head-on collision merger can be correlated with the flux of linear Bondi-momentum at null infinity. In this paper we provide a more sound geometric basis to this picture. First, we show that a rigidity property of dynamical horizons, namely foliation uniqueness, leads to a preferred class of null tetrads and Weyl scalars on these hypersurfaces. Second, we identify a heuristic horizon news-like function, depending only on the geometry of spatial sections of the horizon. Fluxes constructed from this function offer refined geometric quantities to be correlated with Bondi fluxes at infinity, as well as a contact with the discussion of quasi-local 4-momentum on dynamical horizons. Third, we highlight the importance of tracking the internal horizon dual to the apparent horizon in spatial 3-slices when integrating fluxes along the horizon. Finally, we discuss the link between the dissipation of the non-stationary part of the horizons geometry with the viscous-fluid analogy for black holes, introducing a geometric prescription for a slowness parameter in black-hole recoil dynamics.

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 prob- lem 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 [1] 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 qualita- tive 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 [2] 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.

Are Time-Domain Self-Force Calculations Contaminated by Jost Solutions?

The calculation of the self force in the modeling of the gravitational-wave emission from extreme-mass-ratio binaries is a challenging task. Here we address the question of the possible emergence of a persistent spurious solution in time-domain schemes, referred to as a {em Jost junk solution} in the literature, that may contaminate self force calculations. Previous studies suggested that Jost solutions are due to the use of zero initial data, which is inconsistent with the singular sources associated with the small object, described as a point mass. However, in this work we show that the specific origin is an inconsistency in the translation of the singular sources into jump conditions. More importantly, we identify the correct implementation of the sources at late times as the sufficient condition guaranteeing the absence of Jost junk solutions.