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

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

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

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

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 $Z$, 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 $Z$ remain small.Comment: 4 pages, accepted in PR

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