Related papers: The BSSN formulation is a partially constrained ev…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
It is possible to solve the Einstein constraint equations as an evolutionary rather than an elliptic system. Here we consider the Gauss constraint in electrodynamics as a toy model for thist. We use a combination of the evolutionary method…
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for…
General exact solution is obtained for the problem of the development of arbitrary disturbances of the density and velocity in a (1+1)-dimensional universe. This analytical solution may serve, particularly, as a test for numerical methods.…
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside…
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 three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture…
In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the…
The Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…
Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations as a well-posed problem. In general relativity, under certain…
In this paper we propose that the accelerating expansion of the present matter-dominated universe, as suggested by the recent distance measurements of type Ia supernovae, is generated along with the evolution of space in extra dimensions.…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative…
We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity,…