Related papers: Regularization of spherical and axisymmetric evolu…
The lack of regularity of geometric variables at the origin is often a source of serious problem for spherically symmetric evolution codes in numerical relativity. One usually deals with this by restricting the gauge and solving the…
In the absence of symmetry assumptions most numerical relativity simulations adopt Cartesian coordinates. While Cartesian coordinates have some desirable properties, spherical polar coordinates appear better suited for certain applications,…
Brown has recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems. This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation…
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…
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…
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)…
Instabilities in finite difference codes due to the singularity of spherical coordinates at the center are studied. In typical Numerical Relativity applications, standard regularization techniques by themselves do not ensure long term…
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
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…
Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core-collapse, crust and core-quakes and binary mergers and could become detectable either in gravitational waves or high-energy radiation. Here,…
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…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The…
We use the 1+3 frame formalism to write down the evolution equations for spherically symmetric models as a well-posed system of first order PDEs in two variables, suitable for numerical and qualitative analysis.
We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (Quadratic Gravity) in the spherically-symmetric sector. The formulation relies on (i) harmonic gauge to cast the…