Related papers: An Axisymmetric Gravitational Collapse Code
The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (``thorn'') for the…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
Several applications of spectral methods to problems related to the relativistic astrophysics of compact objects are presented. Based on a proper definition of the analytical properties of regular tensorial functions we have developed a…
We present two new solutions to Einstein's equations in (1+5)-spacetime with a positive bulk cosmological constant. One solution has increasing and another solution decreasing bounded scale function without singularities in the range from…
We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We…
We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group…
We report on a new solution to the Einstein-Maxwell equations in 2+1 dimensions with a negative cosmological constant. The solution is static, rotationally symmetric and has a non-zero magnetic field. The solution can be interpreted as a…
Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are found. In even dimensions the solution has many similarities with the…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…
We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397…
Plane symmetric self-similar solutions to Einstein's four-dimensional theory of gravity are studied and all such solutions are given analytically in closed form. The local and global properties of these solutions are investigated and it is…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
We present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…