Geodesic Deviation Equation in Bianchi Cosmologies

We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson-Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor in the GDE.Comment: Submitted to Journal of Physics: Conference Series (JPCS), ERE200

Curvature-spin coupling from the semi-classical limit of the Dirac equation

The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the spin-tensor from internal quantum degrees of freedom, which has a Papapetrou-like coupling with the curvature.Comment: 4 pages, Proceedings of the II Stueckelberg worksho

Dynamics of test bodies with spin in de Sitter spacetime

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma

Analysis of Hamiltonian formulations of linearized General Relativity

The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary. The Hamiltonians and the constraints are different in these two formulations but the structure of the constraint algebra and the gauge invariance derived from it are the same. It is shown that these equivalent Hamiltonian formulations are related to each other by a canonical transformation which is explicitly given. The relevance of these results to the full theory of General Relativity is briefly discussed.Comment: Section Discussion is modified and references are added; 19 page

Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of {\it external} relativistic center of mass can be defined only in terms of the {\it external} Poincar\'e group realization. Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the Poincar\'e group is defined. The three concepts of {\it internal} center of mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An adapted canonical basis of relative variables is found. The invariant mass is the Hamiltonian for the relative motions. In this framework we can introduce the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it spin frame} and {\it canonical spin bases} for the rotational kinematics developed for the non-relativistic N-body problem.Comment: 78 pages, revtex fil

Molecular Physics of Elementary Processes relevant to Hypersonics: atom-molecule, molecule-molecule and atom-surface processes.

In the present chapter some prototype gas and gas-surface processes occurring within the hypersonic flow layer surrounding spacecrafts at planetary entry are discussed. The discussion is based on microscopic dynamical calculations of the detailed cross sections and rate coefficients performed using classical mechanics treatments for atoms, molecules and surfaces. Such treatment allows the evaluation of the efficiency of thermal processes (both at equilibrium and nonequilibrium distributions) based on state-to-state and state specific calculations properly averaged over the population of the initial states. The dependence of the efficiency of the considered processes on the initial partitioning of energy among the various degrees of freedom is discussed

Probing non-Riemannian spacetime geometry

The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.Comment: 8 pages, 1 figure, matches published version including the erratum in Phys. Lett. A 373 (2009) 160

Newton's 2nd Law, Radiation Reaction & Type II Einstein-Maxwell Fields

Considering perturbations off the Reissner-Nordstrom metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we do a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to a rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstrom or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle take the classical form of mass times velocity plus an electromagnetic radiation reaction term while the Bondi mass loss equation become the classical gravitational and electromagnetic (electric and magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation turns into Newtons second law of motion containing the Abraham, Lorentz, Dirac radiation reaction force plus a momentum recoil (rocket) force while the reality condition on the Bondi mass aspect yields the conservation of angular momentum.Comment: 15 page

Curvature invariants in type N spacetimes

Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either vanish, or are constants depending on Lambda. Even all higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are shown to be trivial if a type N spacetime admits a non-expanding and non-twisting null geodesic congruence. However, in the case of expanding type N spacetimes we discover a non-vanishing scalar invariant which is quartic in the second derivatives of the Riemann tensor. We use this invariant to demonstrate that both linearized and the third order type N twisting solutions recently discussed in literature contain singularities at large distances and thus cannot describe radiation fields outside bounded sources.Comment: 17 pages, to appear in Class. Quantum Gra