Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory

TL;DR

This paper extends effective one-body theory to analyze gravitational wave energy flux and waveforms from merging binary black holes with slow spins, providing analytical solutions and detailed waveform characteristics.

Contribution

It introduces a method to include slow spin effects in gravitational wave modeling within the effective one-body framework, deriving analytical solutions for the radial equations.

Findings

Analytical solutions for radial equations of gravitational perturbations.

Expressions for energy flux and waveform modes of slowly spinning binaries.

Dependence of results on second- and third-order spin correction parameters.

Abstract

We extend our research on the energy flux and waveform characteristics of gravitational waves generated by merging nonspinning binary black holes through self-consistent effective one-body theory \cite{L2023} to include binary systems with slowly spinning black holes. Initially, we decompose the equation for the null tetrad component of the gravitationally perturbed Weyl tensor $\psi^B_{4}$ into radial and angular parts, leveraging the second-order approximation of the rotation parameter $a$. Subsequently, we derive an analytical solution for the radial equation and observe that our results are contingent upon the parameters $a_2$, $a_3$ and $a$, which represent the second- and third-order correction parameters, respectively. Ultimately, we calculate the energy flux, the radiation-reaction force and the waveform for the ``plus" and ``cross" modes of the gravitational waves generated by merging slowly spinning binary black holes.