Related papers: Total Collisions in the N-Body Shape Space
In this dissertation we study two well known gravitational scenarios in which singularities may appear; the final state of gravitational collapse and the late time evolution of the universe. In the first scenario, we study a spherically…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We model the gravitational collapse of heavy massive shells including its main quantum corrections. Among these corrections, quantum improvements coming from Quantum Einstein Gravity are taken into account, which provides us with an…
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold. We focus on the case of spherical systems, which are…
The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the…
Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. To date, a century after…
A database on shape evolution of direct N-body models formed out of cold, dissipationless collapse is generated using GRAPE and HARP special purpose computers. Such models are important to understand the formation of elliptical galaxies.…
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological…
The equivalence class of absolute configurations of a system under the group of similarity transformations $Sim(3)$ is called the shape of the system. The $Sim(3)$ invariant Lagrangian of the modified Newtonian theory ensures the existence…
We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one…
The dynamical system constituted by two spherically symmetric thin shells and their own gravitational field is studied. The shells can be distinguished from each other, and they can intersect. At each intersection, they exchange energy on…
We study the spacetime structures of the static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-$\Lambda$ system systematically. We assume the Gauss-Bonnet coefficient $\alpha$ is non-negative. The solutions have the…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…
While studying the continual gravitational collapse of a massive matter cloud in general relativity towards examining collapse final states, an important issue is that of whether shell-crossing singularities can develop as the collapse…