Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes

TL;DR

This paper proposes a cross-correlation method using geometric quantities on black hole horizons and null infinity to analyze strong-field black hole dynamics, especially post-merger recoil effects.

Contribution

It introduces a novel approach linking horizon and null infinity geometries for probing black hole dynamics in a scattering-like framework.

Findings

Demonstrates the method on black hole recoil dynamics

Provides new insights into near-horizon gravitational behavior

Connects horizon geometry with asymptotic gravitational signals

Abstract

The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity and in the geometric characterization of black hole horizons open new conceptual and technical avenues into the problem. We discuss here a research methodology in which spacetime dynamics is probed through the cross-correlation of geometric quantities constructed on the black hole horizon and on null infinity. These two hypersurfaces respond to evolving gravitational fields in the bulk, providing canonical "test screens" in a "scattering"-like perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial Value Problem approach to the construction of generic spacetimes and discuss the role and properties of dynamical trapping horizons as canonical inner "screens" in this context. We apply these ideas and techniques to the study of the recoil dynamics in post-merger binary black holes, an important issue in supermassive galactic black hole mergers.