Related papers: Constructing massive particles surfaces in static …
This article will review quantum particle creation in expanding universes. The emphasis will be on the basic physical principles and on selected applications to cosmological models. The needed formalism of quantum field theory in curved…
We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost surely contains infinitely many copies of…
We construct a hyperbolic sextic surface in P^3(C).
We analyze the structural and dynamical properties of disk-like objects formed in fully consistent cosmological simulations with an inefficient star formation algorithm. Comparison with data of similar observable properties of spiral…
We give a definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of gr-qc/0110014 which show that our…
We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
The geometric transitions from the evolution in the complex plane of time provide channels for particle production for a quantum field in expanding universes. The production rate for one pair is obtained by squaring and summing the…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
We construct stable axially symmetric models of elliptical galaxies. The particle density on phase space for these models depends monotonically on the particle energy and on the third component of the angular momentum. They are obtained as…
We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.
This review is a short introduction to numerical hydrodynamics in a cosmological context, intended for the non specialist. The main processes relevant to galaxy formation are first presented. The fluid equations are then introduced, and…
The gravitational instability of expanding shells is discussed. Linear and nonlinear terms are included in an analytical solution in the static and homogeneous medium. We discuss the interaction of modes and give the time needed for…
We review geometrical properties of a static spacetime $(M,g)$, including geodesic completeness, causality, standard splittings, compact $M$, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic…
We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…
We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.