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

TL;DR

This paper develops a geometric framework for analyzing black-hole horizon dynamics, introducing new quantities and methods to better understand the relation between horizon geometry and gravitational fluxes, with implications for black-hole mergers.

Contribution

It provides a geometric basis for horizon fluxes, identifies a horizon news-like function, and links horizon dissipation to viscous-fluid analogies in black-hole recoil.

Findings

Foliation uniqueness leads to preferred null tetrads and Weyl scalars.

A horizon news-like function is defined based on horizon geometry.

The geometric approach clarifies the relation between horizon fluxes and Bondi fluxes.

Abstract

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 horizon's geometry with the viscous-fluid analogy for black holes, introducing a geometric prescription for a "slowness parameter" in black-hole recoil dynamics.