474 research outputs found
Alternate thematic maps to visualize United Nations Sustainable Development Goal indicator data
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
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