Related papers: Einstein equations in the null quasi-spherical gau…
Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…
We present a code for numerical simulations of the collapse of regular initial data to a black hole in null coordinates. We restrict to twist-free axisymmetry with scalar field matter. Our coordinates are $(u,x,y,\varphi)$, where the…
We construct an analytical approximation for the numerical black hole metric of P. Kanti, et. al. [PRD54, 5049 (1996)] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a…
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…
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…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
We address the hyperboloidal initial value problem in the context of Numerical Relativity, motivated by its evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity, the "location" in spacetime where…
In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions…
We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on…
The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of…
We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the…
Observation and characterisation of gravitational waves from binary black holes requires accurate knowledge of the expected waveforms. The late inspiral and merger phase of the waveform is obtained through direct numerical integration of…
The semiclassical Einstein equations are solved to first order in $\epsilon = \hbar/M^2$ for the case of an extreme or nearly extreme Reissner-Nordstr\"{o}m black hole perturbed by the vacuum stress-energy of quantized free fields. It is…
We consider the initial value problem for a massless scalar field in the Schwarzschild geometry. When constructed using a complex-frequency approach the necessary Green's function splits into three components. We discuss all of these in…
We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation (3G)…
Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a…
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field…
Gravitational-wave black-hole spectroscopy provides a unique opportunity to test the strong-field regime of gravity and the nature of the final object formed in the aftermath of a merger. Here we investigate the prospects for black-hole…
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can…
A new semi-supervised machine learning package is introduced which successfully solves the Euclidean vacuum Einstein equations with a cosmological constant, without any symmetry assumptions. The model architecture contains subnetworks for…