490 research outputs found
Expanding perfect fluid generalizations of the C-metric
We reexamine Petrov type D gravitational fields generated by a perfect fluid
with spatially homogeneous energy density and in which the flow lines form a
timelike non-shearing and non-rotating congruence. It is shown that the
anisotropic such spacetimes, which comprise the vacuum C-metric as a limit
case, can have \emph{non-zero} expansion, contrary to the conclusion in the
original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class
consists of cosmological models with generically one and at most two Killing
vectors. We construct their line element and discuss some important properties.
The methods used in this investigation incite to deduce testable criteria
regarding shearfree normality and staticity op Petrov type spacetimes in
general, which we add in an appendix.Comment: 16 pages, extended and amended versio
Levi-Civita,Tullio
International audienceTullio Levi-Civita (29 March 1873 to 29 December 1941) has been an Italian mathematician and mathematical physicist, known above all for his work on the absolute differential calculus. Levi-Civita came from a rigorous and creative school of mathematical physicists and was a pupil of Gregorio Ricci-Curbastro. LeviCivita’s work included outstanding results in pure and applied mathematics and in celestial and analytic mechanics but also celebrated textbooks. These last, even those written in Italian, have influenced mathematical physicists all over the world.Levi-Civita has perfected some conceptual tools of great importance in modern science, particularly in general relativity, number theory, and continuum mechanics
Operational significance of the deviation equation in relativistic geodesy
Deviation equation: Second order differential equation for the 4-vector which
measures the distance between reference points on neighboring world lines in
spacetime manifolds.
Relativistic geodesy: Science representing the Earth (or any planet),
including the measurement of its gravitational field, in a four-dimensional
curved spacetime using differential-geometric methods in the framework of
Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy".
arXiv admin note: text overlap with arXiv:1811.1047
On the Geometry of Surface Stress
We present a fully general derivation of the Laplace--Young formula and
discuss the interplay between the intrinsic surface geometry and the extrinsic
one ensuing from the immersion of the surface in the ordinary euclidean
three-dimensional space. We prove that the (reversible) work done in a general
surface deformation can be expressed in terms of the surface stress tensor and
the variation of the intrinsic surface metric
Comments on photonic shells
We investigate in detail the special case of an infinitely thin static
cylindrical shell composed of counter-rotating photons on circular geodetical
paths separating two distinct parts of Minkowski spacetimes--one inside and the
other outside the shell--and compare it to a static disk shell formed by null
particles counter-rotating on circular geodesics within the shell located
between two sections of flat spacetime. One might ask whether the two cases are
not, in fact, merely one
Possible way out of the Hawking paradox: Erasing the information at the horizon
We show that small deviations from spherical symmetry, described by means of
exact solutions to Einstein equations, provide a mechanism to "bleach" the
information about the collapsing body as it falls through the aparent horizon,
thereby resolving the information loss paradox. The resulting picture and its
implication related to the Landauer's principle in the presence of a
gravitational field, is discussed.Comment: 11 pages, Latex. Some comments added to answer to some raised
questions. Typos corected. Final version, to appear in Int. J. Modern. Phys.
Levi-Civita cylinders with fractional angular deficit
The angular deficit factor in the Levi-Civita vacuum metric has been
parametrized using a Riemann-Liouville fractional integral. This introduces a
new parameter into the general relativistic cylinder description, the
fractional index {\alpha}. When the fractional index is continued into the
negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder
and in an Israel shell.Comment: 5 figure
Magnetic Strings in Dilaton Gravity
First, I present two new classes of magnetic rotating solutions in
four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type
potential. The first class of solutions yields a 4-dimensional spacetime with a
longitudinal magnetic field generated by a static or spinning magnetic string.
I find that these solutions have no curvature singularity and no horizons, but
have a conic geometry. In these spacetimes, when the rotation parameter does
not vanish, there exists an electric field, and therefore the spinning string
has a net electric charge which is proportional to the rotation parameter. The
second class of solutions yields a spacetime with an angular magnetic field.
These solutions have no curvature singularity, no horizon, and no conical
singularity. The net electric charge of the strings in these spacetimes is
proportional to their velocities. Second, I obtain the ()-dimensional
rotating solutions in Einstein-dilaton gravity with Liouville-type potential. I
argue that these solutions can present horizonless spacetimes with conic
singularity, if one chooses the parameters of the solutions suitable. I also
use the counterterm method and compute the conserved quantities of these
spacetimes.Comment: 16 pages, no figure, references added, some minor correction
Quasi-BiHamiltonian Systems and Separability
Two quasi--biHamiltonian systems with three and four degrees of freedom are
presented. These systems are shown to be separable in terms of Nijenhuis
coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with
an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis
coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May
1997
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Modelling and Analysis of Vibrations in a UAV Helicopter with a Vision System
The analysis of the nature and damping of unwanted vibrations on Unmanned Aerial Vehicle (UAV) helicopters are important tasks when images from on‐board vision systems are to be obtained. In this article, the authors model a UAV system, generate a range of vibrations originating in the main rotor and design a control methodology in order to damp these vibrations. The UAV is modelled using VehicleSim, the vibrations that appear on the fuselage are analysed to study their effects on the on‐board vision system by using Simmechanics software. Following this, the authors present a control method based on an Adaptive Neuro‐Fuzzy Inference System (ANFIS) to achieve satisfactory damping results over the vision system on board
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