Related papers: Towards a Singularity-Proof Scheme in Numerical Re…
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
I present a fast algorithm to find apparent horizons. This algorithm uses an explicit representation of the horizon surface, allowing for arbitrary horizon resolutions and, in principle, shapes. Novel in this approach is that the tensor…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
Penrose's singularity theorem implies that if a trapped region forms in a gravitational collapse, then a singularity must form as well within such region. However, it is widely expected that singularities should be generically avoided by…
We investigate what are the key physical features that cause the development of a naked singularity, rather than a black hole, as the end-state of spherical gravitational collapse. We show that sufficiently strong shearing effects near the…
We present a new numerical code that evolves a spherically symmetric configuration of collisionless matter in the Brans-Dicke theory of gravitation. In this theory the spacetime is dynamical even in spherical symmetry, where it can contain…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing…
This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such…
We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are…
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…
Numerical studies of gravitational collapse in isotropic coordinates have recently shown an interesting connection between the gravitational Lagrangian and black hole thermodynamics. A study of the actual spacetime was not the main focus of…
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…
An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove…