Hamiltoniane di effective one body per binarie coalescenti con spin allineati

TEOBResumS and SEOBNRv4 are the two mainstream analytical waveform models that accurately describe the dynamics of two coalescing compact objects of masses m1 and m2 and spins S1 and S2 aligned to the orbital angular momentum, up to merger and ringdown. Both use the effective-one-body (EOB) approach to the relative dynamics, though improved by Numerical Relativity (NR) similations. The EOB method maps the real relative dynamics of two objects into the effective dynamics of a (spinning) particle of mass \mu=m1 m2/(m1+m2) moving in a deformed Kerr metric. Under this approach, the post-Newtonian expanded Hamiltonian is resummed in special ways in order to improve its behavior and its predictability in the strong-field, fast-velocity regimes up to the merger. The aim of this work is to compare in detail the analytical choices made in the two models. Chapter 1 encompasses an introduction to the physics of gravitational waves, giving an overview of their theoretical foundations and exploring some of their potentialities. In Chapter 2 an analysis of the Hamiltonian of a spinning particle at linear order in the particle's spin orbiting a Kerr black hole is done. The EOB approach builds on a deformed Kerr metric, and it is therefore useful and pedagogical to recall the structure of the Hamiltonian of a perticle on Kerr space-time. In Chapter 3 the EOB method is described by showing the procedure that maps the two-body PN-expanded Hamiltonian describing the relative motion into the Hamiltonian describing the motion of an effective particle moving into an effective potential. In Chapter 4 the analytical structure of TEOBResumS, the first state-of-the-art EOB model that we will focus on, is shown. In Chapter 5 SEOBNRv4, the second state-of-the-art EOB model, is presented. It is shown, for the first time, that its analytical structure can be reshaped and moulded in order to establish a direct correspondence with the analytical structure of TEOBResumS. This is related to the possibility, pointed out here for the first time, to introduce a centrifugal radius (i.e. a single function that divides the orbital angular momentum in the Hamiltonian) also in SEOBNRv4, likewise TEOBResumS. In Chapter 6 the Hamiltonians of TEOBResumS and SEOBNRv4 are compared with a particular attention on the metric functions and the gauge choices. From the analysis we found that the main structural differences between the two models is, precisely, the structure of the centrifugal radius. In TEOBResumS it is given by a natural deformation of the same quantity defined on the Kerr metric. By contrast, in SEOBNRv4 this naturaleness is lost. On top of this, we explicitly connect the spin gauges used and the various analytical structures. In Chapter 7 the last stable circular orbit, or innermost stable circular orbit in the EOB models, is analyzed, exploring its sensitivity to changes in the various functions (e.g. resummation of the potential, spin-orbit coupling etc.). Finally, in Chapter 8 the post-Adiabatic approximation is applied.