Redshift Factor and the First Law of Binary Black Hole Mechanics in Numerical Simulations

2016/06/30 by Aaron Zimmerman, Adam G. M. Lewis, Harald P. Pfeiffer +1 · 3 citations
Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Astrophysics #Binary black hole #Binary number #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology #Gravitational wave #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Redshift #Theoretical physics #gr-qc

paper · pdf · doi:10.1103/physrevlett.117.191101

published as Phys. Rev. Lett. 117, 191101 (2016) · 7 pages, 4 figures. Updated to reflect published version

arxiv created 2016/10/25 · openalex publication_date 2016/11/04 · arxiv updated 2016/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The redshift factor z is an invariant quantity of fundamental interest in post-Newtonian and self-force descriptions of compact binaries. It connects different approximation schemes, and plays a central role in the first law of binary black hole mechanics, which links local quantities to asymptotic measures of energy and angular momentum in these systems. Through this law, the redshift factor is conjectured to have a close relation to the surface gravity of the event horizons of black holes in circular orbits. We propose and implement a novel method for extracting the redshift factor on apparent horizons in numerical simulations of quasicircular binary inspirals. Our results confirm the conjectured relationship between z and the surface gravity of the holes and that the first law holds to a remarkable degree for binary inspirals. The redshift factor enables tests of analytic predictions for z in spacetimes where the binary is only approximately circular, giving a new connection between analytic approximations and numerical simulations.

Citations

• Approximate Killing Fields as an Eigenvalue Problem
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Cited by

• Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry
• Black holes, gravitational waves and fundamental physics: a roadmap
• Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio