Related papers: Numerical Relativity in Spherical Polar Coordinate…
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…
One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost…
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…
The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum…
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…
The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of…
We develop a 3 dimensional computer code to study a coalescing neutron star binary. The code can currently follow the evolution up to two stars begin to merge from two spherical stars of mass 1 solar mass and radius 8.9km with separation…
We report on work using a newly developed code, SpheriCo.jl, that computes the gravitational collapse of a spherical scalar field, where the scalar can be either a classical field, or a quantum field operator. By utilising…
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented.…
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…
We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same as those in [Mori-Tanaka], yet we believe…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, {\sc CosmoGRaPH}, which employs the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism on a…
With the advent of relativistic mechanics, the Lorentz transformation replaced the Galilean transformation based on classical Newtonian mechanics among inertial frames at high uniform velocities, but both transformations are based on…
Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features --- a high order of convergence in regions where the solution is smooth…
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…
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
Using minimalist assumptions we develop a natural functional decomposition for the spacetime metric, and explicit tractable formulae for the surface gravities, in arbitrary stationary circular (PT symmetric) axisymmetric spacetimes. We…