The next generation of gravitational-wave detectors will require waveform models that are both substantially longer and substantially more accurate than those used for current ground-based observations. This requirement is especially important for massive binary black holes observed by the Laser Interferometer Space Antenna (LISA), for which signals can remain in band for hundreds to thousands of orbits and can accumulate signal-to-noise ratios large enough that small modeling errors become measurable. At this accuracy, waveform modeling is not only a problem of improving individual approximation schemes. It is also a problem of constructing controlled interfaces between the different descriptions used to model a binary black hole. This dissertation develops a framework for constructing LISA-accurate binary-black-hole waveforms by connecting post-Newtonian theory, numerical relativity, and black-hole perturbation theory in a consistent way. The first part of the dissertation formulates the LISA-driven accuracy requirements and develops a post-Newtonian--numerical-relativity hybridization framework for producing long waveforms. In this framework, the waveforms are compared at future null infinity after fixing the Bondi--Metzner--Sachs frame, and the intrinsic post-Newtonian parameters are determined as part of the matching procedure rather than assumed to be identical to the quasi-local parameters used to label the numerical-relativity simulation. This construction makes waveform hybridization not only a method for extending waveform duration, but also a diagnostic of asymptotic-frame errors, numerical errors, post-Newtonian truncation errors, and parameter-definition errors. The second part of the dissertation addresses the parameter-definition problem directly. The masses and spins used in post-Newtonian theory, numerical relativity, and black-hole perturbation theory are physically meaningful within their own constructions, but they are not automatically identical at finite binary separation. To relate these quantities from first principles, this dissertation develops a strong-field matching framework in which black-hole perturbation theory provides the local inner-zone description near each black hole. By constructing gauge-preserving coordinate transformations between local comoving coordinates and the global coordinates used by post-Newtonian theory or numerical relativity, the framework relates point-particle parameters, local black-hole parameters, and quasi-local horizon quantities through the spacetime geometry itself. This provides a route toward parameter maps that can be used in waveform hybridization, numerical-relativity catalogs, and gravitational-wave inference. The final part of the dissertation develops analytical and numerical infrastructure needed for this program. On the analytical side, the dissertation studies the convergence and regime of validity of high-order post-Newtonian information by comparing successive post-Newtonian truncation orders with a long, high-accuracy numerical-relativity simulation after BMS-frame fixing and parameter fitting. This comparison identifies the velocity range in which higher post-Newtonian orders improve agreement with numerical relativity and the region near merger where the expansion loses quantitative reliability. On the numerical side, the dissertation develops gauge boundary conditions in the Spectral Einstein Code that suppress long-timescale coordinate drift in binary-black-hole simulations, improving the quality of the numerical data needed for precision hybridization and strong-field matching. Together, these results show that LISA-accurate waveform modeling requires simultaneous control of waveform length, asymptotic frame, intrinsic parameter definitions, post-Newtonian truncation error, and numerical gauge effects. The dissertation therefore provides a framework in which hybridization, strong-field parameter matching, and gauge-controlled numerical relativity become complementary parts of a single program for precision binary-black-hole waveform modeling.
Dongze Sun (Tue,) studied this question.