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The nature of binary black hole coalescence is the final, uncharted frontier of the relativistic Kepler problem. In the United States, binary black hole coalescence has been identified as a computational ``Grand Challenge'' whose solution…
We study the method for generating the initial data of black hole systems in Gauss-Bonnet (GB) gravity. The initial data are assumed to be momentarily static and conformally flat. Although the equation for the conformal factor is highly…
Coalescing compact object binaries consisting of black holes and/or Neutron stars are a prime target for ground-based gravitational wave detectors. This article reviews the status of numerical simulations of these systems, with an emphasis…
We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains…
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
Coalescing massive black hole binaries are produced by the mergers of galaxies. The final stages of the black hole coalescence produce strong gravitational radiation that can be detected by the space-borne LISA. In cases where the black…
As the compact binary catalog continues to grow rapidly, developing and refining tests to probe the nature of compact objects is essential for a comprehensive understanding of both the observed data and the underlying astrophysics of the…
We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to…
Primordial black holes, if considered to constitute a significant fraction of cold dark matter, trace the inhomogeneous large-scale structure of the Universe. Consequently, the stochastic gravitational-wave background, originating from…
We describe the first convergent numerical method to determine static black hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a family of solutions parametrized by the ratio of the black hole size and the size of the…
Tremendous progress has been made towards the solution of the binary-black-hole problem in numerical relativity. The waveforms produced by numerical relativity will play a role in gravitational wave detection as either test-beds for…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal…
We propose a novel method to test the binary black hole (BBH) nature of compact binaries detectable by gravitational wave (GW) interferometers and hence constrain the parameter space of other exotic compact objects. The spirit of the test…
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…
Binary black holes occupy a special place in our quest for understanding the evolution of galaxies along cosmic history. If massive black holes grow at the center of (pre-)galactic structures that experience a sequence of merger episodes,…
We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex…
In X-ray binaries, several percent of the compact object luminosity is intercepted by the surface of the normal companion and re-radiated through Compton reflection and the K-fluorescence. This reflected emission follows the variability of…
We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner…
We present a detailed, fully nonlinear study of binary systems involving one black hole and one boson star, considering the effects of both a quartic self-interaction and a solitonic potential for the scalar field. First, we show the…