Comparing Effective One Body Hamiltonians for spin-aligned coalescing binaries

TL;DR

This paper compares two semi-analytical gravitational waveform models, TEOBResumS and SEOBNRv4, focusing on their Hamiltonians for spin-aligned black hole binaries, revealing differences in spin effects and demonstrating efficient waveform generation.

Contribution

It provides an analytical comparison of the Hamiltonians underlying TEOBResumS and SEOBNRv4 models, introducing a new form of the SEOBNRv4 Hamiltonian and exploring its computational advantages.

Findings

The Hamiltonians differ mainly in their spin effect implementations.

A new centrifugal radius formulation for SEOBNRv4 Hamiltonian is proposed.

Post-adiabatic approximation enables long-inspiral waveform generation with low computational cost.

Abstract

TEOBResumS and SEOBNRv4 are the two existing semi-analytical gravitational waveform models for spin-aligned coalescing black hole binaries based on the effective-one-body approach.They are informed by numerical relativity simulations and provide the relative dynamics and waveforms from early inspiral to plunge, merger and ringdown The central building block of each model is the EOB resummed Hamiltonian.The two models implement different Hamiltonians that are both deformations of the Hamiltonian of a test spinning black hole moving around a Kerr black hole.Here we analytically compare, element by element, the two Hamiltonians. In particular: we illustrate that one can introduce a centrifugal radius SEOBNRv4, so to rewrite the Hamiltonian in a more compact form that is analogous to the one of TEOBResumS.The latter centrifugal radius cannot, however, be identified with the one used in TEOBResumS because the two models differ in their ways of incorporating spin effects in their respective deformations of the background Kerr Hamiltonian. We performed extensive comparisons between the energetics corresponding to the two Hamiltonians using gauge-invariant quantities. Finally, as an exploratory investigation, we apply the post-adiabatic approximation to the newly rewritten SEOBNRv4 Hamiltonian, illustrating that it is possible to generate long-inspiral waveforms with negligible computational cost.