Related papers: Numerical Relativity Using a Generalized Harmonic …
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
We present a code for numerical simulations of the collapse of regular initial data to a black hole in null coordinates. We restrict to twist-free axisymmetry with scalar field matter. Our coordinates are $(u,x,y,\varphi)$, where the…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
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 have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN…
Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on…
We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral…
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…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
A new lattice based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (eg. a set of leg lengths on a simplicial lattice) but it differs significantly in the way that the…
Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of…
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,…
We present tests and results of a new axisymmetric, fully general relativistic code capable of solving the coupled Einstein-matter system for a perfect fluid matter field. Our implementation is based on the Bondi metric, by which the…
I propose an alternative $f(R)$ theory of gravity constructed by applying the function $f$ directly to the Ricci tensor instead of the Ricci scalar. The main goal of this study is to derive the resulting modified Einstein equations for the…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
We follow a new pathway to the definition of the Stochastic Quantization (SQ), first proposed by Parisi and Wu, of the action functional yielding the Einstein equations. Hinging on the functional similarities between the Ricci-Flow equation…