200 research outputs found
The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces
We reformulate the standard local equations of general relativity for
asymptotically flat spacetimes in terms of two non-local quantities, the
holonomy around certain closed null loops on characteristic surfaces and
the light cone cut function , which describes the intersection of the future
null cones from arbitrary spacetime points, with future null infinity. We
obtain a set of differential equations for and equivalent to the vacuum
Einstein equations. By finding an algebraic relation between and this
set of equations is reduced to just two coupled equations: an
integro-differential equation for which yields the conformal structure of
the underlying spacetime and a linear differential equation for the ``vacuum''
conformal factor. These equations, which apply to all vacuum asymptotically
flat spacetimes, are however lengthy and complicated and we do not yet know of
any solution generating technique. They nevertheless are amenable to an
attractive perturbative scheme which has Minkowski space as a zeroth order
solution.Comment: 28 pages, RevTeX, 3 PostScript figure
Ecuador's Economy Since 2007
Outside observers could be forgiven for expecting Ecuador to suffer terribly during and after the recent global crisis. Two of the country's largest sources of foreign earnings, petroleum exports and remittances from abroad, crashed during the global recession. Furthermore, lacking its own currency, the government's options for responding were limited. But instead of a deep, protracted recession, Ecuador lost only 1.3 percent of GDP during three quarters of contraction. After four additional quarters the economy returned to the pre-recession level of output, and two years after the recession started, it reached its 20-year growth trend
Asymptotically Shear-free and Twist-free Null Geodesic Congruences
We show that, though they are rare, there are asymptotically flat space-times
that possess null geodesic congruences that are both asymptotically shear- free
and twist-free (surface forming). In particular, we display the class of
space-times that possess this property and demonstrate how these congruences
can be found. A special case within this class are the Robinson- Trautman
space-times. In addition, we show that in each case the congruence is isolated
in the sense that there are no other neighboring congruences with this dual
property.Comment: 10 page
Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines
We show that for asymptotically vanishing Maxwell fields in Minkowski space
with non-vanishing total charge, one can find a unique geometric structure, a
null direction field, at null infinity. From this structure a unique complex
analytic world-line in complex Minkowski space that can be found and then
identified as the complex center of charge. By ''sitting'' - in an imaginary
sense, on this world-line both the (intrinsic) electric and magnetic dipole
moments vanish. The (intrinsic) magnetic dipole moment is (in some sense)
obtained from the `distance' the complex the world line is from the real space
(times the charge). This point of view unifies the asymptotic treatment of the
dipole moments For electromagnetic fields with vanishing magnetic dipole
moments the world line is real and defines the real (ordinary center of
charge). We illustrate these ideas with the Lienard-Wiechert Maxwell field. In
the conclusion we discuss its generalization to general relativity where the
complex center of charge world-line has its analogue in a complex center of
mass allowing a definition of the spin and orbital angular momentum - the
analogues of the magnetic and electric dipole moments.Comment: 17 page
The Real Meaning of Complex Minkowski-Space World-Lines
In connection with the study of shear-free null geodesics in Minkowski space,
we investigate the real geometric effects in real Minkowski space that are
induced by and associated with complex world-lines in complex Minkowski space.
It was already known, in a formal manner, that complex analytic curves in
complex Minkowski space induce shear-free null geodesic congruences. Here we
look at the direct geometric connections of the complex line and the real
structures. Among other items, we show, in particular, how a complex world-line
projects into the real Minkowski space in the form of a real shear-free null
geodesic congruence.Comment: 16 page
Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
In classical electromagnetic theory, one formally defines the complex dipole
moment (the electric plus 'i' magnetic dipole) and then computes (and defines)
the complex center of charge by transforming to a complex frame where the
complex dipole moment vanishes. Analogously in asymptotically flat space-times
it has been shown that one can determine the complex center of mass by
transforming the complex gravitational dipole (mass dipole plus 'i' angular
momentum) (via an asymptotic tetrad trasnformation) to a frame where the
complex dipole vanishes. We apply this procedure to such space-times which are
asymptotically stationary or static, and observe that the calculations can be
performed exactly, without any use of the approximation schemes which must be
employed in general. In particular, we are able to exactly calculate complex
center of mass and charge world-lines for such space-times, and - as a special
case - when these two complex world-lines coincide, we recover the Dirac value
of the gyromagnetic ratio.Comment: 11 page
Center of Mass and spin for isolated sources of gravitational radiation
We define the center of mass and spin of an isolated system in General
Relativity. The resulting relationships between these variables and the total
linear and angular momentum of the gravitational system are remarkably similar
to their Newtonian counterparts, though only variables at the null boundary of
an asymptotically flat spacetime are used for their definition. We also derive
equations of motion linking their time evolution to the emitted gravitational
radiation. The results are then compared to other approaches. In particular one
obtains unexpected similarities as well as some differences with results
obtained in the Post Newtonian literature . These equations of motion should be
useful when describing the radiation emitted by compact sources such as
coalescing binaries capable of producing gravitational kicks, supernovas, or
scattering of compact objects.Comment: 16 pages. Accepted for publication in Phys. Rev.
Astrophysical limits on quantum gravity motivated birefringence
We obtain observational upper bounds on a class of quantum gravity related
birefringence effects, by analyzing the presence of linear polarization in the
optical and ultraviolet spectrum of some distant sources. In the notation of
Gambini and Pullin we find .Comment: 4 pages, submitted to Phys. Rev. Let
Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum
The purpose of this work is to return, with a new observation and rather
unconventional point of view, to the study of asymptotically flat solutions of
Einstein equations. The essential observation is that from a given
asymptotically flat space-time with a given Bondi shear, one can find (by
integrating a partial differential equation) a class of asymptotically
shear-free (but, in general, twistiing) null geodesic congruences. The class is
uniquely given up to the arbitrary choice of a complex analytic world-line in a
four-parameter complex space. Surprisingly this parameter space turns out to be
the H-space that is associated with the real physical space-time under
consideration. The main development in this work is the demonstration of how
this complex world-line can be made both unique and also given a physical
meaning. More specifically by forcing or requiring a certain term in the
asymptotic Weyl tensor to vanish, the world-line is uniquely determined and
becomes (by several arguments) identified as the `complex center-of-mass'.
Roughly, its imaginary part becomes identified with the intrinsic spin-angular
momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall
Null Surfaces and Legendre Submanifolds
It is shown that the main variable Z of the Null Surface Formulation of GR is
the generating function of a constrained Lagrange submanifold that lives on the
energy surface H=0 and that its level surfaces Z=const. are Legendre
submanifolds on that energy surface.
The behaviour of the variable Z at the caustic points is analysed and a
genralization of this variable is discussed.Comment: 28 pages, 7 figure
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