Comparing effective-one-body Hamiltonians for spin-aligned coalescing binaries

TEOBResumS and SEOBNRv4 are the two existing semianalytical gravitational waveform models for spin-aligned coalescing black hole binaries based on the effective-one-body (EOB) 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, clement by clement, the two Hamiltonians. In particular: we illustrate that one can introduce a centrifiigal radius in 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 postadiabatic approximation to the newly rewritten SEOBNRv4 Hamiltonian, illustrating that it is possible to generate long-inspiral waveforms with negligible computational cost.