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A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Frans Pretorius

Recent gravitational wave (GW) detections showing signatures of eccentricity and spin precession underscore the need to model binary black holes (BBHs) possessing these features simultaneously. Most efforts over the past fifteen years to…

General Relativity and Quantum Cosmology · Physics 2026-04-13 Tom Colin , Sashwat Tanay , Laura Bernard

We analyze in detail the spin precession equations in binary black hole systems, when the tidal torque on a Kerr black hole due to quadrupole-monopole coupling is taken into account. We show that completing the precession equations with…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Etienne Racine

We present a highly accurate, fully analytical model for the late inspiral, merger, and ringdown of black-hole binaries with arbitrary mass ratios and spin vectors, including the contributions of harmonics beyond the fundamental mode. This…

General Relativity and Quantum Cosmology · Physics 2019-05-22 Sean T. McWilliams

Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…

General Relativity and Quantum Cosmology · Physics 2014-10-06 Alexandre Le Tiec

We analytically solve the constraints in General Relativity for two black holes with arbitrary momenta and spin up to third order in these parameters. We compute the location and geometry of the apparent horizon, which depend on the spins,…

General Relativity and Quantum Cosmology · Physics 2025-09-16 Leyla Ogurol , Tore Boybeyi , Bayram Tekin

We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron…

Gravitational waves from spin-precessing binaries exhibit amplitude oscillations that provide an invaluable method to extract the spins of the inspiraling compact objects. The spin-spin and spin-orbit interactions that cause this effect are…

General Relativity and Quantum Cosmology · Physics 2018-10-03 Nicholas Loutrel , Takahiro Tanaka , Nicolas Yunes

Spin precession occurs in binary black holes whose spins are misaligned with the orbital angular momentum. Otherwise, the spin configuration is constant and the subsequent binary dynamics and gravitational-wave emission are much simpler. We…

General Relativity and Quantum Cosmology · Physics 2021-05-03 Matthew Mould

We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We…

General Relativity and Quantum Cosmology · Physics 2012-02-22 David A. Nichols , Yanbei Chen

The current paradigm for constructing waveforms from precessing compact binaries is to first construct a waveform in a non-inertial, co-precessing binary source frame followed by a time-dependent rotation to map back to the physical,…

General Relativity and Quantum Cosmology · Physics 2020-05-20 Antoni Ramos-Buades , Patricia Schmidt , Geraint Pratten , Sascha Husa

We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Nicolas Yunes , Wolfgang Tichy

We introduce a new general-relativistic timing observable that measures the breaking of reflection symmetry in photon arrival times caused by black hole spin. Using backward ray tracing in the Kerr spacetime, we construct time-delay maps…

High Energy Astrophysical Phenomena · Physics 2026-05-14 Shakibul Chowdhury

Based on the covariant hamiltonian formalism, we study the dynamics of spinning test bodies in the Kerr and Schwarzschild spacetimes. For the first time, we derive the exact solution of circular orbits in the Kerr plane without truncating…

General Relativity and Quantum Cosmology · Physics 2021-09-22 Satish Kumar Saravanan

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Frans Pretorius

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…

General Relativity and Quantum Cosmology · Physics 2010-12-06 Chad R. Galley , Frank Herrmann , John Silberholz , Manuel Tiglio , Gustavo Guerberoff

We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass…

General Relativity and Quantum Cosmology · Physics 2011-07-19 Michael D. Hartl , Alessandra Buonanno

We revisit the three black hole scenario with numerical relativity techniques to study hierarchical configurations where the inner binary contains highly spinning black holes. We find that the merger time of the binary gets a delay (with a…

General Relativity and Quantum Cosmology · Physics 2024-06-19 Giuseppe Ficarra , Carlos O. Lousto

Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that "up-down" binaries, in which the spin of the heavier (lighter) black hole is aligned…

General Relativity and Quantum Cosmology · Physics 2021-03-10 Vijay Varma , Matthew Mould , Davide Gerosa , Mark A. Scheel , Lawrence E. Kidder , Harald P. Pfeiffer

We present new insights into the phenomenology of post-Newtonian spin precession in black-hole binaries. Using multi-timescale methods, previous work has shown that the precession and nutation dynamics in such systems can be classified into…

General Relativity and Quantum Cosmology · Physics 2025-08-28 Davide Gerosa , Giulia Foroni , Giulia Fumagalli , Emanuele Berti