Related papers: A polytopal discrete de Rham scheme for the exteri…
In previous paper, we present an SO(3) Wu-Yang-like Kaluza-Klein dyon so- lution satisfies the Einstein equation in the seven-dimensional spacetimes. In this note, we will show an alternative approach using an orthonormal frame, the…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be…
We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages…
In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
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…
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…
A formulation of elliptic boundary value problems is used to develop the first discrete exterior calculus (DEC) library for massively parallel computations with 3D domains. This can be used for steady-state analysis of any physical process…
A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…
We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These…
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
The aim of this article is to derive discontinuous finite elements vector spaces which can be put in a discrete de-Rham complex for which an harmonic gap property may be proven. First, discontinuous finite element spaces inspired by…
Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3+1 decomposition for the zero vorticity case for arbitrary spatially…