15,308 research outputs found
An Exact Universal Gravitational Lensing Equation
We first define what we mean by gravitational lensing equations in a general
space-time. A set of exact relations are then derived that can be used as the
gravitational lens equations in all physical situations. The caveat is that
into these equations there must be inserted a function, a two-parameter family
of solutions to the eikonal equation, not easily obtained, that codes all the
relevant (conformal) space-time information for this lens equation
construction. Knowledge of this two-parameter family of solutions replaces
knowledge of the solutions to the geodesic equations.
The formalism is then applied to the Schwarzschild lensing problemComment: 12 pages, submitted to Phys. Rev.
A nonstationary generalization of the Kerr congruence
Making use of the Kerr theorem for shear-free null congruences and of
Newman's representation for a virtual charge ``moving'' in complex space-time,
we obtain an axisymmetric time-dependent generalization of the Kerr congruence,
with a singular ring uniformly contracting to a point and expanding then to
infinity. Electromagnetic and complex eikonal field distributions are naturally
associated with the obtained congruence, with electric charge being
necesssarily unit (``elementary''). We conjecture that the corresponding
solution to the Einstein-Maxwell equations could describe the process of
continious transition of the naked ringlike singularitiy into a rotating black
hole and vice versa, under a particular current radius of the singular ring.Comment: 6 pages, twocolum
The Theory of Caustics and Wavefront Singularities with Physical Applications
This is intended as an introduction to and review of the work of V, Arnold
and his collaborators on the theory of Lagrangian and Legendrian submanifolds
and their associated maps. The theory is illustrated by applications to
Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null
surfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include
On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.Comment: 25 pages, LaTex, a shortened version, including a new proof for lemma
5.1, the additional case of Einstein-Yang-Mills-Higgs systems is also
covered, to appear in Class. Quant. Gra
Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity
A new quasigroup approach to conservation laws in general relativity is
applied to study asymptotically flat at future null infinity spacetime. The
infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to
the Poincar\'e quasigroup and the Noether charge associated with any element of
the Poincar\'e quasialgebra is defined. The integral conserved quantities of
energy-momentum and angular momentum are linear on generators of Poincar\'e
quasigroup, free of the supertranslation ambiguity, posess the flux and
identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page
Maxwell Fields and Shear-Free Null Geodesic Congruences
We study and report on the class of vacuum Maxwell fields in Minkowski space
that possess a non-degenerate, diverging, principle null vector field (null
eigenvector field of the Maxwell tensor) that is tangent to a shear-free null
geodesics congruence. These congruences can be either surface forming (the
tangent vectors proportional to gradients) or not, i.e., the twisting
congruences. In the non-twisting case, the associated Maxwell fields are
precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from
an electric monopole moving on an arbitrary worldline. The null geodesic
congruence is given by the generators of the light-cones with apex on the
world-line. The twisting case is much richer, more interesting and far more
complicated. In a twisting subcase, where our main interests lie, it can be
given the following strange interpretation. If we allow the real Minkowski
space to be complexified so that the real Minkowski coordinates x^a take
complex values, i.e., x^a => z^a=x^a+iy^a with complex metric g=eta_abdz^adz^b,
the real vacuum Maxwell equations can be extended into the complex and
rewritten as curlW =iWdot, divW with W =E+iB. This subcase of Maxwell fields
can then be extended into the complex so as to have as source, a complex
analytic world-line, i.e., to now become complex Lienard-Wiechart fields. When
viewed as real fields on the real Minkowski space, z^a=x^a, they possess a real
principle null vector that is shear-free but twisting and diverging. The twist
is a measure of how far the complex world-line is from the real 'slice'. Most
Maxwell fields in this subcase are asymptotically flat with a time-varying set
of electric and magnetic moments, all depending on the complex displacements
and the complex velocities.Comment: 3
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
Image distortion in non perturbative gravitational lensing
We introduce the idea of {\it shape parameters} to describe the shape of the
pencil of rays connecting an observer with a source lying on his past
lightcone. On the basis of these shape parameters, we discuss a setting of
image distortion in a generic (exact) spacetime, in the form of three {\it
distortion parameters}. The fundamental tool in our discussion is the use of
geodesic deviation fields along a null geodesic to study how source shapes are
propagated and distorted on the path to an observer. We illustrate this
non-perturbative treatment of image distortion in the case of lensing by a
Schwarzschild black hole. We conclude by showing that there is a
non-perturbative generalization of the use of Fermat's principle in lensing in
the thin-lens approximation.Comment: 22 pages, 6 figures, to appear in Phys. Rev. D (January 2001
Small-World Networks: Links with long-tailed distributions
Small-world networks (SWN), obtained by randomly adding to a regular
structure additional links (AL), are of current interest. In this article we
explore (based on physical models) a new variant of SWN, in which the
probability of realizing an AL depends on the chemical distance between the
connected sites. We assume a power-law probability distribution and study
random walkers on the network, focussing especially on their probability of
being at the origin. We connect the results to L\'evy Flights, which follow
from a mean field variant of our model.Comment: 11 pages, 4 figures, to appear in Phys.Rev.
Using synchronization to improve earthquake forecasting in a cellular automaton model
A new forecasting strategy for stochastic systems is introduced. It is
inspired by the concept of anticipated synchronization between pairs of chaotic
oscillators, recently developed in the area of Dynamical Systems, and by the
earthquake forecasting algorithms in which different pattern recognition
functions are used for identifying seismic premonitory phenomena. In the new
strategy, copies (clones) of the original system (the master) are defined, and
they are driven using rules that tend to synchronize them with the master
dynamics. The observation of definite patterns in the state of the clones is
the signal for connecting an alarm in the original system that efficiently
marks the impending occurrence of a catastrophic event. The power of this
method is quantitatively illustrated by forecasting the occurrence of
characteristic earthquakes in the so-called Minimalist Model.Comment: 4 pages, 3 figure
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