arXiv subjects

Ezra T. Newman

Publications and source records attributed to Ezra T. Newman.

At least 19 recordsLinked to original sources

arXiv2017

Light-Cones, Almost Light-Cones and Almost-Complex Light-Cones

We point out an unusual relationship among a variety of null geodesic congruences; (a) the generators of ordinary light-cones and (b) certain (related) shear-free but twisting congruences in Minkowski Space-time as well as (c) asymptotically shear-free null geodesic congruences that exist in the neighborhood of Penrose's Scri in Einstein or Einstein-Maxwell asymptotically flat-space-times. We refer to these geodesic congruences respectively as: Lignt-Cones (LCs), as Almost-Complex- Light-Cones, (ACLCs), [though they are real they resemble complex light-cones in complex Minkowski space] and finally to a family of congruences in asymptotically flat-spaces as `Almost Light-Cones', (ALC). The two essential points of resemblance among the three families are: (1) they are all either shear-free or asymptotically shear-free and (2) in each family the individual members of the family can be labeled by the points in a real or complex four-dimensional manifold. As an example, the Minkowski space LCs are labeled by the (real) coordinate value of their apex. In the case of (ACLCs) (complex coordinate values), the congruences will have non-vanishing twist whose magnitude is determined by the imaginary part of the complex coordinate values. In studies of gravitational radiation, Bondi-type of null surfaces and their associated Bondi coordinates have been almost exclusively used for calculations. Some surprising relations arise if, instead of the Bondi coordinates, one uses ALCs and their associated coordinate systems in the analysis of the Einstein-Maxwell equations near Scri. More explicitly and surprisingly, the asymptotic Bianchi Identities expressed in the coordinates of the ALCs, turn directly into many of the standard definitions and relations of classical mechanics.

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arXiv2017

Surprising Structures Hiding at Penrose's Future Null Infinity

Since the late1950s, almost all discussions of Asymptotically Flat (Einstein-Maxwell) Space-Times have taken place in the context of Penrose's Null Infinity, $\mathcal{I}^{+}.$\ $\ $In addition,\ almost all calculations have used the Bondi coordinate and tetrad systems. \ We show - first, that there are other natural coordinate systems, near $\mathcal{I}^{+},$ (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). \ Using these new coordinates and their associated tetrad, we \textit{define the complex dipole moment, i.e., as the mass dipole plus i times angular momentum,} from the $l=1,\ $harmonic coefficient of a component of the asymptotic$\ $Weyl tensor. Second, from this definition, from the Bianchi Identities and from the Bondi mass and linear momentum, we show that \ there exists a large number of results - identifications and dynamics - identical to those of classical mechanics and electrodynamics. They include, among many others, \textbf{P}=M\textbf{v}+..., \textbf{L}=\textbf{r}x\textbf{P}, \ spin, Newtons 2nd Law with the Rocket force term (M\textbf{v}) and radiation reaction, angular momentum conservation and others. \ All these relations take place in the rather mysterious H-Space.

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arXiv2016

Asymptotically Flat Space-Times and its Hidden Recesses: An Enigma from GR

We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) Asymptotically Flat Space-Times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of NU (Newman-Unti) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-Space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-Space and its dual space H. 1

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arXiv2013

On Integrating the Left-Flat Vacuum Einstein Equations

Considering the spin-coefficient version of the left-flat vacuum Einstein equations, all but one of the fifty equations can be explicitly integrated via the introduction of five spin-weight s=-2 complex potentials. The final equation is a non-linear wave equation for the last of the potentials. Solutions to this equation determine solutions for the entire system. Solutions for several special cases are obtained

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arXiv2011

Newton's 2nd Law, Radiation Reaction & Type II Einstein-Maxwell Fields

Considering perturbations off the Reissner-Nordstrom metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we do a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to a rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstrom or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle take the classical form of mass times velocity plus an electromagnetic radiation reaction term while the Bondi mass loss equation become the classical gravitational and electromagnetic (electric and magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation turns into Newtons second law of motion containing the Abraham, Lorentz, Dirac radiation reaction force plus a momentum recoil (rocket) force while the reality condition on the Bondi mass aspect yields the conservation of angular momentum.

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arXiv2010

NP Stokes fields for radio astronomy

The spin weighted spherical harmonic (SWSH) description of angular functions typically is associated with the Newman-Penrose (NP) null tetrad formalism. Recently the SWSH description, but not the NP formalism, has been used in the study of the polarization anisotropy of the cosmic microwave background. Here we relate this application of SWSHs to a description of electromagnetic radiation and polarization in the NP formalism. In particular we introduce NP Stokes fields that are the NP equivalent of the Stokes parameters. In addition to giving a more coherent foundation for the recent cosmological SWSH application, the NP formalism aids in the computation of the Lorentz transformation properties of polarization.

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arXiv2008

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.

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arXiv2007

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.

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arXiv2005

Asymptotic twistor Theory and the Kerr Theorem

We first review asymptotic twistor theory with its real subspace of null asymptotic twistors. This is followed by a description of an asymptotic version of the Kerr theorem that produces regular asymptotically shear free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes.

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arXiv2005

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.

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arXiv2005

Twisting Null Geodesic Congruences and the Einstein-Maxwell Equations

The purpose of the present work is to extend the earlier results for asymptotically flat vacuum space-times to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically shear-free null geodesic congruences depending on a complex world-line in the same four-dimensional complex space. However in this case there will be, in general, two distinct but uniquely chosen world-lines. One of which can be assigned as the complex center-of- charge while the other could be called the complex center of mass. Rather than investigating the situation where there are two distinct complex world-lines, we study instead the special degenerate case where the two world-lines coincide, i.e., where there is a single unique world-line. This mimics the case of algebraically special Einstein-Maxwell fields where the degenerate principle null vector of the Weyl tensor coincides with a Maxwell principle null vector. Again we obtain equations of motion for this world-line - but explicitly found here only in an approximation. Though there are ambiguities in assigning physical meaning to different terms it appears as if reliance on the Kerr and charged Kerr metrics and classical electromagnetic radiation theory helps considerably in this identification. In addition, the resulting equations of motion appear to have many of the properties of a particle with intrinsic spin and an intrinsic magnetic dipole moment. At first order there is even the classical radiation-reaction term 2/3{q^{2}}{c^{-3}}ddot{v}, now obtained without any use of the Lorentz force law but obtained directly from the asymptotic fields themselves. One even sees the possible suppression, via the Bondi mass loss, of the classical runaway solutions due to the radiation reaction force.

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arXiv2005

Tensorial Spin-s Harmonics

We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many calculations in General Relativity. In the calculations, products of these functions, with their needed decompositions which are given here, often arise naturally.

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arXiv2005

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.

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arXiv2005

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.

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arXiv2004

Cartan Normal Conformal Connections from Pairs of 2nd Order PDE's

We explore the different geometric structures that can be constructed from the class of pairs of 2nd order PDE's that satisfy the condition of a vanishing generalized Wünschmann invariant. This condition arises naturally from the requirement of a vanishing torsion tensor. In particular, we find that from this class of PDE's we can obtain all four-dimensional conformal Lorentzian metrics as well as all Cartan normal conformal O(4,2) connections. To conclude, we briefly discuss how the conformal Einstein equations can be imposed by further restricting our class of PDE's to those satisfying additional differential conditions.

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arXiv2002

Dynamics of Fermat potentials in non-perturbative gravitational lensing

We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we derive two lens equations: one for the case of thick compact lenses and the other one for lensing by gravitational waves. These equations in principle generalize the astrophysical scheme for lensing by removing the thin-lens approximation while retaining the weak fields.

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arXiv2002

Fermat Potentials for Non-Perturbative Gravitational Lensing

The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which relates the placement and distortion of the images to the real source position in the thin-lens scenario, is obtained by extremizing the time of arrival among all the null paths from the source to the observer (Fermat's principle). We show that the construction of envelopes of certain families of null surfaces consitutes an alternative variational principle or version of Fermat's principle that leads naturally to a lens equation in a generic spacetime with any given metric. We illustrate the construction by deriving the lens equation for static asymptotically flat thin lens spacetimes. As an application of the approach, we find the bending angle for moving thin lenses in terms of the bending angle for the same deflector at rest. Finally we apply this construction to cosmological spacetimes (FRW) by using the fact they are all conformally related to Minkowski space.

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arXiv2002

On a Classical, Geometric Origin of Magnetic Moments, Spin-Angular Momentum and the Dirac Gyromagnetic Ratio

By treating the real Maxwell Field and real linearized Einstein equations as being imbedded in complex Minkowski space, one can interpret magnetic moments and spin-angular momentum as arising from a charge and mass monopole source moving along a complex world line in the complex Minkowski space. In the circumstances where the complex center of mass world-line coincides with the complex center of charge world-line, the gyromagnetic ratio is that of the Dirac electron.

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