Related papers: Embedding initial data for black hole collisions
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 explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a…
We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two…
We compute the shadows of colliding black holes using the Kastor-Traschen cosmological multiblack hole solution that is an exact solution describing the collision of maximally charged black holes with a positive cosmological constant. We…
We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and…
We study head-on collisions of unequal mass black hole binaries in D=5 space-time dimensions, with mass ratios between 1:1 and 1:4. Information about gravitational radiation is extracted by using the Kodama-Ishibashi gauge-invariant…
The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results…
We study isometric embeddings of non-extremal Reissner-Nordstr\"om metric describing a charged black hole. We obtain three new embeddings in the flat ambient space with minimal possible dimension. These embeddings are global, i.e.…
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace…
We present a new numerical code developed for the evolution of binary black-hole spacetimes using different initial data and evolution techniques. The code is demonstrated to produce state-of-the-art simulations of orbiting and inspiralling…
We study the problem of simultaneous geometric embedding of two paths without self-intersections on an integer grid. We show that minimizing the length of the longest edge of such an embedding is NP-hard. We also show that we can minimize…
The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic and extrinsic geometry. To do this, we use the parabolic partial differential equation for…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
Time-symmetric initial data for two-body solutions in three dimensional anti-deSitter gravity are found. The spatial geometry has constant negative curvature and is constructed as a quotient of two-dimensional hyperbolic space. Apparent…
We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about…
Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes:…
We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a…
We discuss a sequence of numerically constructed geometries describing binary black hole event horizons -- providing the necessary input for characteristic evolution of the exterior spacetime. Our sequence approaches a single Schwarzschild…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…