Related papers: Evolution of a periodic eight-black-hole lattice i…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver…
We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection…
Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology,…
It is known how to choose initial data for Einstein's equations describing an arbitrary number of black holes at a moment of time symmetry. This idea has been used to give insight into the cosmological averaging problem. We study the local…
Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining…
We construct time-dependent multi-centre solutions to three-dimensional general relativity with zero or negative cosmological constant. These solutions correspond to dynamical systems of freely falling black holes and conical singularities,…
We consider the problem of constructing cosmological solutions of the Einstein-Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct…
The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce…
Lattice universes are spatially closed space-times of spherical topology in the large, containing masses or black holes arranged in the symmetry of a regular polygon or polytope. Exact solutions for such spacetimes are found in 2+1…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
The construction of black-hole lattices, first attempted by Richard Lindquist and John Wheeler in 1957, has recently been tackled with renewed interest, as a test bed for studying the behavior of inhomogeneities in the context of the…
Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about 8000M, where M is the mass of the black hole. This degree of stability is achieved by using growth-rate…
Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter"…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
One of the main issues in gravitation is the presence of singularities in the most common space-time solutions of General Relativity, as the case of black holes. A way of constructing regular solutions that remove spacelike singularities…
The evolution of black-hole binaries in vacuum spacetimes constitutes the two-body problem in general relativity. The solution of this problem in the framework of the Einstein field equations is a substantially more complex exercise than…
In this paper we explore the idea that black holes can persist in a universe that collapses to a big crunch and then bounces into a new phase of expansion. We use a scalar field to model the matter content of such a universe {near the time}…
The time evolution of black holes involves both the canonical equations of quantum gravity and the statistical mechanics of Hawking radiation, neither of which contains a time variable. In order to introduce the time, we apply the…