Related papers: Numerical simulations of generic singuarities
I discuss empty space, as it appears in the physical foundations of relativistic field theories and in the semiclassical study of isolated systems. Of particular interest is the relationship between empirical measurements of the…
We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
In this paper we discuss computer simulations of de Sitter and anti de Sitter spacetimes, which are maximally symmetric, relativistic analogs of non-Euclidean geometries. We present prototype games played in these spacetimes; such games and…
Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with…
The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing…
We describe a numerical approach to address the BKL conjecture that the generic cosmological singularity is locally Mixmaster-like. We consider application of a symplectic PDE solver to three models of increasing complexity--spatially…
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static…
Vacuum static, axially symmetric space-times in $D$-dimensional general relativity with a Ricci-flat internal space are discussed. It is shown, in particular, that some of the monopole-type solutions are free of curvature singularities and…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an…
Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this…
Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant…
We review the classical and quantum singularity structure of a broad class of spacetimes with asymptotically power-law behavior near the origin. Quantum considerations "heal" a large class of scalar curvature singularities.
To probe naked spacetime singularities with waves rather than with particles we study the well-posedness of initial value problems for test scalar fields with finite energy so that the natural function space of initial data is the Sobolev…
We study the evolution of bubble spacetimes in vacuum and electrovac scenarios by numerical means. We find strong evidence against the formation of naked singularities in (i) scenarios with negative masses displaying initially collapsing…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…