Related papers: Black Hole Excision with Multiple Grid Patches
We present details of a new numerical code designed to study the formation and evaporation of 2-dimensional black holes within the CGHS model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of…
We reinvestigate the utility of time-independent constant mean curvature foliations for the numerical simulation of a single spherically-symmetric black hole. Each spacelike hypersurface of such a foliation is endowed with the same constant…
We present an efficient numerical algorithm for evolving self-gravitating systems of dark-matter particles that leverages the assumption of spherical symmetry to reduce the nominally six-dimensional phase space to three dimensions. It can…
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used,…
Through an illuminating thought experiment we demonstrate that the nonsingular "continued collapse" picture of a black hole is the only consistent and physical one. We provide a class exact solutions on the boundary of the space of physical…
We review in generality why time-independent endstates can be reached in black hole and collapse simulations, with and without excision. We characterise the Killing states of the Bona-Masso slicing condition with time derivative along the…
We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
Massive black holes (BHs) inhabiting galactic nuclei can be described by two parameters only, i.e. mass and spin, that change through cosmic time in response to accretion and merger events. While most numerical simulations accurately track…
Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology,…
We present a discussion of the periodicity in imaginary time of maximally extended black hole spacetimes without reference to Euclidean manifolds. As motivation, we first demonstrate our approach for the Rindler geometry in flat space…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
In General Relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to lowest order in spin, as the metrics of stellar objects; (ii) they are independent of mass, when expressed in geometric units;…
We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a…
Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a $d$-dimensional tensor product space, the number of grid points is $N = \mathcal O(h^{-1} |\log h|^{d-1})$, where $h$ is a mesh parameter. The…
The images of supermassive black holes surrounded by optically-thin, radiatively-inefficient accretion flows, like those observed with the Event Horizon Telescope, are characterized by a bright ring of emission surrounding the black-hole…
We study time evolution of rotating, axisymmetric, two dimensional inviscid accretion flows around black holes using a grid based finite difference method. We do not use reflection symmetry on the equatorial plane in order to inspect if the…
Multi-black hole solutions play a relevant role both from the theoretical and the phenomenological point of view. In this Thesis, we construct some regular multi-black hole spacetimes in pure Einstein's General Relativity with the aid of…
We will present results of a long term stable evolution, to $t=1000m$, of a maximally sliced Schwarzschild blackhole using a smooth lattice method.