Related papers: Implicit-explicit (IMEX) evolution of single black…
As a network of advanced-era gravitational wave detectors is nearing its design sensitivity, efficient and accurate waveform modeling becomes more and more relevant. Understanding of the nature of the signal being sought can have an order…
Implicit-Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is partitioned into stiff and nonstiff processes with the goal of lower computational costs than a purely…
We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93,…
We construct a fully analytic, general relativistic, nonspinning black hole binary spacetime that approximately solves the vacuum Einstein equations everywhere in space and time for black holes sufficiently well separated. The metric is…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced decomposition is introduced. With this decomposition, the requirement of a small enough residual in the…
For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlying conservation laws. On the other hand, implicit methods…
To describe a general bound binary black hole system, we need to consider orbital eccentricity and the misalignment of black holes' spin vectors with respect to the orbital angular momentum. While binary black holes produced through many…
Direct electromagnetic observation of the orbital motion of a sub-parsec, supermassive black hole binary (SMBHB) would provide the first conclusive proof of such systems existing. Widely considered to be the sources of gravitational waves,…
We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the…
Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code…
We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral…
The late stage of the inspiral of two black holes may have important non-Newtonian effects that are unrelated to radiation reaction. To understand these effects we approximate a slowly inspiralling binary by a stationary solution to…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
Modeling of large populations of binary stellar systems is an intergral part of a many areas of astrophysics, from radio pulsars and supernovae to X-ray binaries, gamma-ray bursts, and gravitational-wave mergers. Binary population synthesis…
The properties of precessing, coalescing binary black holes are presently inferred through comparison with two approximate models of compact binary coalescence. In this work we show these two models often disagree substantially when…
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<\beta<1$. From the known structure of the non-smooth solution and by introducing corresponding…