Related papers: Axisymmetric Numerical Relativity
We describe a method of implementing the axisymmetric evolution of general-relativistic hydrodynamics and magnetohydrodynamics through modification of a multipatch grid scheme. In order to ease the computational requirements required to…
The 2+1+1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an…
We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of…
We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical,…
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…
Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
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…
We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial…
This thesis focuses on the application of numerical relativity methods to the solutions of problems in strong gravity. Our goal is the study of mergers of compact objects in the strong field regime where non-linear dynamics manifest and…
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to…
We solve Einstein's field equations coupled to relativistic hydrodynamics in full 3+1 general relativity to evolve astrophysical systems characterized by strong gravitational fields. We model rotating, collapsing and binary stars by…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The…
We present a new evolution system for Einstein's field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the…
We investigate the dimensional reduction of 3+1 vacuum axisymmetric Einstein's equations to 2+1 dimensional Einstein-wave map system and observe that the resulting system is 1) not asymptotically flat, 2) its geometric-mass diverges and 3)…