Related papers: Evolving a puncture black hole with fixed mesh ref…
We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
We solve the Hamiltonian and momentum constraints of general relativity for two black holes with nearly extremal spins and relativistic boosts in the puncture formalism. We use a non-conformally-flat ansatz with an attenuated superposition…
We have developed a new numerical code to study the evolution of distorted, rotating black holes. We discuss the numerical methods and gauge conditions we developed to evolve such spacetimes. The code has been put through a series of tests,…
We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $(\alpha_0,\beta_0)$, and use…
We extend a new finite element code, Einstein PHG (iPHG), to solve the evolution part of Einstein equations in first-order GH formalism. This paper is the third one of a systematic investigation of applying adaptive finite element method to…
This work is part of an ongoing research programme to study possible Primordial Black Hole (PBH) formation during the radiation dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
We discuss refinement criteria for the Berger-Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole merger simulations. We compare three different strategies: the…
We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with…
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…
The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows…
Dynamical black holes in the non-perturbative regime are not mathematically well understood. Studying approximate symmetries of spacetimes describing dynamical black holes gives an insight into their structure. Utilising the property that…
The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…