Related papers: Three Dimensional Numerical Relativity with a Hype…
We consider a $(4 + 2k)$ - dimensional Einstein-Gauss-Bonnet model with the cosmological $\Lambda$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional…
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented.…
We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can…
In 1900, Macfarlane proposed a hyperbolic variation on Hamilton's quaternions that closely resembles Minkowski spacetime. Viewing this in a modern context, we expand upon Macfarlane's idea and develop a model for real hyperbolic 3-space in…
We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
In order to perform accurate and stable long-time numerical integration of the Einstein equation, several hyperbolic systems have been proposed. We here present numerical comparisons between weakly hyperbolic, strongly hyperbolic, and…
We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
We investigate the possibility to approximate relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic…
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite…
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein…
We discuss possible observational manifestations of static, spherically symmetric solutions of a class of multidimensional theories of gravity, which includes the low energy limits of supergravities and superstring theories as special…
We include matter sources in Einstein's field equations and show that our recently proposed 3+1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution…
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…
Here we prove a global existence theorem for sufficiently small however fully nonlinear perturbations of a family of background solutions of the $`n+1$' vacuum Einstein equations in the presence of a positive cosmological constant…