Related papers: The numerical relativity breakthrough for binary b…
Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of…
Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the…
Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing…
The first attempts at solving a binary black hole spacetime date back to the 1960s, with the pioneering works of Hahn and Lindquist. In spite of all the computational advances and enormous efforts by several groups, the first stable,…
The two-body problem in general relativity is reviewed, focusing on the final stages of the coalescence of the black holes as uncovered by recent successes in numerical solution of the field equations.
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…
We study the post-Newtonian dynamics of black hole binaries in Einstein-scalar-Gauss-Bonnet gravity theories. To this aim we build static, spherically symmetric black hole solutions at fourth order in the Gauss-Bonnet coupling $\alpha$. We…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
We discuss a new N-body simulation method for studying black hole binary dynamics. This method avoids previous numerical problems due to large mass ratios and trapped orbits with short periods. A treatment of relativistic effects is…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
The advent of long-term stability in numerical relativity has yielded a windfall of answers to long-standing questions regarding the dynamics of space-time, matter, and electromagnetic fields in the strong-field regime of black-hole binary…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future…
Gravitational waves from merging binary black holes present exciting opportunities for understanding fundamental aspects of gravity, including nonlinearities in the strong-field regime. One challenge in studying and interpreting the…
We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of…
We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used…
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…
The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently…
Gravitational waves radiated during binary black hole coalescence is a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole…