Related papers: Differential Forms and Wave Equations for General …
Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible…
We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures.…
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
The present work has a double aim. On the one hand we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincar\'e Gauge Theory. On the other hand…
We develop a non-linear distributional renormalisation algebra for Gaussian Quantum Foam, built from sequences of scaled Gaussians on spacelike hypersurfaces of homotopic, globally hyperbolic spacetimes and their distributional limits. The…
A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
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 a systematic framework for computing frequency-domain gravitational waveforms from relativistic binary scattering in different asymptotic regimes. The method yields a controlled series expansion that can in principle be extended…
The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a…
We present a comprehensive theoretical framework for gravitational wave (GW) propagation and their \textbf{nonlinear backreaction} in $f(R, G)$ modified gravity. By developing a scalar-tensor formulation with two auxiliary fields, we…
The Standard Model plus gravitation is derived from general relativity with three dimensions of time. I claim that when the Lagrangian for general relativity is calculated using three dimensions of time, the unified field theory results. I…
We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conceptually simple construction of fundamental solution…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function…
The non-linear dynamics of irrotational dust in General Relativity is studied in synchronous and comoving coordinates. All the equations are written in terms of the metric tensor of spatial sections orthogonal to the flow, which allows an…