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We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…
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…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
The use of compactified hyperboloidal coordinates for metric formulations of the Einstein field Equations introduces formally singular terms in the equations of motion whose numerical treatment requires care. In this paper we study a…
We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…
Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity . This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are…
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…
The Good-Bad-Ugly-F model is a system of semi-linear wave equations that mimics the asymptotic form of the Einstein field equations in generalized harmonic gauge with specific constraint damping and suitable gauge source functions. These…
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…
We describe the first axisymmetric numerical code based on the generalized harmonic formulation of the Einstein equations which is regular at the axis. We test the code by investigating gravitational collapse of distributions of complex…
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…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
We present simulations of the Einstein-Maxwell-Klein-Gordon system on compactified hyperboloidal slices. To the best of our knowledge, this is the first time that this setup is evolved with a common formulation like BSSN/Z4. Hyperboloidal…
This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…
A mathematical model is constructed for the evolution of spherical perturbations in a cosmological one-component statistical system of completely degenerate scalarly charged fermions with a scalar Higgs interaction. A complete system of…
Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity.…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…