70 research outputs found
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
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
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
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
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Electromagnetic Induced Gravitational Perturbations
We study the physical consequences of two diffferent but closely related
perturbation schemes applied to the Einstein-Maxwell equations. In one case the
starting space-time is flat while in the other case it is Schwarzschild. In
both cases the perturbation is due to a combined electric and magnetic dipole
field. We can see, within the Einstein-Maxwell equations a variety of physical
consequences. They range from induced gravitational energy-momentum loss, to a
well defined spin angular momentum with its loss and a center-of-mass with its
equations of motion.Comment: 1
Large quantum gravity effects and nonlocal variables
We reconsider here the model where large quantum gravity effects were first
found, but now in its Null Surface Formulation (NSF). We find that although the
set of coherent states for , the basic variable of NSF, is as restricted as
it is the one for the metric, while some type of small deviations from these
states may cause huge fluctuations on the metric, the corresponding
fluctuations on remain small.Comment: 4 pages, accepted in PR
Electrodynamic Radiation Reaction and General Relativity
We argue that the well-known problem of the instabilities associated with the
self-forces (radiation reaction forces) in classical electrodynamics are
possibly stabilized by the introduction of gravitational forces via general
relativity
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
The Large Footprints of H-Space on Asymptotically Flat Space-Times
We show that certain structures defined on the complex four dimensional space
known as H-Space have considerable relevance for its closely associated
asymptotically flat real physical space-time. More specifically for every
complex analytic curve on the H-space there is an asymptotically shear-free
null geodesic congruence in the physical space-time. There are specific
geometric structures that allow this world-line to be chosen in a unique
canonical fashion giving it physical meaning and significance.Comment: 7 page
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