Numerical evolution of the center of mass and angular momentum for binaries black holes

TL;DR

This paper tests the Kozameh-Quiroga formalism for evolving global variables like center of mass and angular momentum during black hole binary coalescence, using numerical simulations to validate its accuracy.

Contribution

It applies the K-Q formalism to numerical data of black hole mergers, demonstrating its consistency with existing results and providing a new method for tracking global variables.

Findings

The equations of motion produce trajectories consistent with numerical data.

Final physical variables match Rochester metadata results.

The formalism effectively models the evolution of global variables during mergers.

Abstract

The asymptotic approach derived by Kozameh-Quiroga (K-Q) provides a modern framework to obtain the evolution of global variables of isolated sources of gravitational radiation. We test the K-Q formalism evolving the equations of motion for the center of mass, the intrinsic angular momentum, and several other global variables, for black hole binary coalescence. First we evolve the equations of motion using 777 simulations from the RIT catalogue numerical data of $\psi_4$ [J. Healy and C.O. Lousto, Third RIT binary black hole simulations catalog, Phys. Rev. D 102, 104018 (2020).]. We then analyze the trajectory of the center of mass and compute the final state of other physical variables after the coalescence has taken place. Finally, we show the results obtained from our equations of motion are consistent with those in the Rochester metadata.