2,285 research outputs found
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects
This is the first of a couple of papers in which, by exploiting the
capabilities of the Hamiltonian approach to general relativity, we get a number
of technical achievements that are instrumental both for a disclosure of
\emph{new} results concerning specific issues, and for new insights about
\emph{old} foundational problems of the theory. The first paper includes: 1) a
critical analysis of the various concepts of symmetry related to the
Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian
viewpoint, on the other. This analysis leads, in particular, to a
re-interpretation of {\it active} diffeomorphisms as {\it passive and
metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose the (nearly unknown) connection of
a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a
re-visitation of the canonical reduction of the ADM formulation of general
relativity, with particular emphasis on the geometro-dynamical effects of the
gauge-fixing procedure, which amounts to the definition of a \emph{global
(non-inertial) space-time laboratory}. This analysis discloses the peculiar
\emph{dynamical nature} that the traditional definition of distant simultaneity
and clock-synchronization assume in general relativity, as well as the {\it
gauge relatedness} of the "conventions" which generalize the classical
Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde
Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller
The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the development of cartography, highlighting the main ideas that are related to quasiconformality. Some of these ideas were completely ignored in the previous historical surveys on quasiconformal mappings. We then survey early quasiconformal theory in the works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller, which are the 20th-century founders of the theory
Convex regions in the plane and their domes
We make a detailed study of the relation of a euclidean convex region to . The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of . The first result is to prove that the nearest point retraction is 2-quasiconformal. The second is to establish precise estimates of the distortion of near
A supersymmetric D-brane Model of Space-Time Foam
We present a supersymmetric model of space-time foam with two stacks of eight
D8-branes with equal string tensions, separated by a single bulk dimension
containing D0-brane particles that represent quantum fluctuations in the
space-time foam. The ground state configuration with static D-branes has zero
vacuum energy. However, gravitons and other closed-string states propagating
through the bulk may interact with the D0-particles, causing them to recoil and
the vacuum energy to become non zero. This provides a possible origin of dark
energy. Recoil also distorts the background metric felt by energetic massless
string states, which travel at less than the usual (low-energy) velocity of
light. On the other hand, the propagation of chiral matter anchored on the D8
branes is not affected by such space-time foam effects.Comment: 33 pages, latex, five figure
Effect of Peculiar Motion in Weak Lensing
We study the effect of peculiar motion in weak gravitational lensing. We
derive a fully relativistic formula for the cosmic shear and the convergence in
a perturbed Friedmann Universe. We find a new contribution related to galaxies
peculiar velocity. This contribution does not affect cosmic shear in a
measurable way, since it is of second order in the velocity. However, its
effect on the convergence (and consequently on the magnification, which is a
measurable quantity) is important, especially for redshifts z < 1. As a
consequence, peculiar motion modifies also the relation between the shear and
the convergence.Comment: 11 pages, 7 figures; v2: discussion on the reduced shear added (5.C),
additional references, version accepted in PRD; v3: mistakes corrected in
eqs. (26), (31), (33) and (44); results unchange
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