Related papers: Embedding initial data for black hole collisions
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
We perform both distorted black hole evolutions and binary black hole head on collisions and compare the results of using a full grid to results obtained by excising the black hole interiors. In both cases the evolutions are found to run…
The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging prob- lem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black- hole horizons…
We study global flat embeddings inside and outside of event horizons of black holes such as Schwarzschild and Reissner-Nordstr\"{o}m black holes, and of de Sitter space. On these overall patches of the curved manifolds we investigate four…
The standard approach to the numerical evolution of black hole data using the ADM formulation with maximal slicing and vanishing shift is extended to non-symmetric black hole data containing black holes with linear momentum and spin by…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
The conformally flat families of initial data typically used in numerical relativity to represent boosted black holes are not those of a boosted slice of the Schwarzschild spacetime. If such data are used for each black hole in a collision,…
We present a numerical-relativity study of comparable-mass boson star-black hole (BS-BH) head-on collisions, focusing on both initial-data construction and gravitational-wave (GW) phenomenology. We show that plain superposition can strongly…
Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically…
We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild…
We evaluate how much energy can be converted into gravitational radiation in head-on collision of black holes. We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint…
The initial phase of the inspiral process of a binary black-hole system can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph, contributes. In this talk we report how all…
Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…