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Black Hole Mergers as the Fastest Photon Ring Scramblers

D. Giataganas, G. F. Giudice, A. Ianniccari, A. J. Iovino, A. Kehagias, F. Quevedo, D. Perrone, A. Riotto

Abstract

Black holes are the most efficient scramblers in nature. By mapping the instantaneous mass and angular momentum of two spinless black holes in a quasi-circular binary onto those of an effective Kerr black hole, we demonstrate that the final state of the merger remnant corresponds with remarkable accuracy to the configuration that renders null geodesics unstable at the highest possible rate. This suggests a deep connection between the properties of black holes resulting from binary mergers and their unstable null orbits.

Black Hole Mergers as the Fastest Photon Ring Scramblers

Abstract

Black holes are the most efficient scramblers in nature. By mapping the instantaneous mass and angular momentum of two spinless black holes in a quasi-circular binary onto those of an effective Kerr black hole, we demonstrate that the final state of the merger remnant corresponds with remarkable accuracy to the configuration that renders null geodesics unstable at the highest possible rate. This suggests a deep connection between the properties of black holes resulting from binary mergers and their unstable null orbits.
Paper Structure (4 sections, 49 equations, 1 figure)

This paper contains 4 sections, 49 equations, 1 figure.

Table of Contents

  1. Kerr metric and equatorial reduction
  2. Rindler induced metric form, and the effective temperature
  3. The radial and polar potentials and the Mino time
  4. Impact of the unknown fifth-order post-Newtonian correction

Figures (1)

  • Figure 1: Left Panel: The averaged Lyapunov coefficient $\overline{\lambda}_{\rm p}$, rescaled by $(1+q)$, as a function of the binary angular momentum for several mass ratios $q$. Stars indicate the locations of the maxima. The vertical lines indicate the values obtained from the numerical fit in Eq. (\ref{['fit']}), once the final binary mass has been rescaled from $M_f=M(j_*)$ to $M_\mathrm{tot}$. Right Panel: Relative difference $\delta$ between the numerical values $J_{f}$ and the values that maximize $\overline{\lambda}_{\rm p}$, as a function of the mass ratio $q$.