arXiv subjects

E. T. Newman

Publications and source records attributed to E. T. Newman.

15 recordsLinked to original sources

arXiv2016

The Kerr-Newman metric: A Review

The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of this metric from the Reissner-Nordstrom solution by means of a complex transformation algorithm and provide a brief overview of its basic geometric properties. We also include some discussion of interpretive issues, related metrics, and higher-dimensional analogues.

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arXiv2012

Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation

Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.

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arXiv2011

Light cones in relativity: Real, complex and virtual, with applications

We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity acts as a "holographic screen," interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex world-line; a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinity (center of mass, spin, angular momentum, linear momentum, force) are given kinematic meaning and dynamical descriptions in terms of the complex world-line.

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arXiv2010

The Generalized Good Cut Equation

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this note to study these equations and show their relationship to each other. In particular we show how they all have a four complex dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.

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arXiv2009

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.

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arXiv2009

Vacuum non-expanding horizons and shear-free null geodesic congruences

We investigate the geometry of a particular class of null surfaces in space-time called vacuum Non-Expanding Horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex world-line in a complex four dimensional space, each such choice induces a CR structure on the horizon, and a particular world-line (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.

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arXiv2009

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.

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arXiv2008

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.

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arXiv2008

On Extracting Physical Content from Asymptotically Flat Space-Time Metrics

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g., degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates) or from solutions that have symmetries or approximate symmetries. In the present work we will be concerned with asymptotically flat space times where the approximate symmetry is the Bondi-Metzner-Sachs (BMS) group. For these spaces the Bondi four-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat space-times, we give kinematic meaning to the Bondi four-momentum. In other words we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin-vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux.

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arXiv2007

The Geometry of Regular Shear-Free Null Geodesic Congruences, CR functions and their Application to the Flat-Space Maxwell Equations

We describe here what appears to be a new structure that is hidden in all asymptotically vanishing Maxwell fields possessing a non-vanishing total charge. Though we are dealing with real Maxwell fields on real Minkowski space nevertheless, directly from the asymptotic field one can extract a complex analytic world-line defined in complex Minkowski space that gives a unified Lorentz invariant meaning to both the electric and magnetic dipole moments. In some sense the world-line defines a `complex center of charge' around which both electric and magnetic dipole moments vanish. The question of how and where does this complex world-line arise is one of the two main subjects of this work. The other subject concerns what is known in the mathematical literature as a CR structure. In GR, CR structures naturally appear in the physical context of shear-free (or asymptotically shear-free) null geodesic congruences in space-time. For us, the CR structure is associated with the embedding of Penrose's real three-dimensional null infinity, I^+, as a surface in a two complex dimensional space, C^2. It is this embedding, via a complex function, (a CR function), that is our other area of interest. Specifically we are interested in the `decomposition' of the CR function into its real and imaginary parts and the physical information contained in this decomposition.

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arXiv2006

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.

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arXiv2006

On the Physical Meaning of the Robinson-Trautman-Maxwell Fields

We study the Robinson-Trautman-Maxwell Fields in two closely related coordinate systems, the original Robinson-Trautman (RT) coordinates (in a more general context, often referred to as NU coordinates) and Bondi coordinates. In particular, we identify one of the RT variables as a velocity and then from the Bondi energy-momentum 4-vector, we find kinematic expressions for the mass and momentum in terms of this velocity. From these kinematic expressions and the energy-momentum loss equation we obtain surprising equations of motion for `the center of mass' of the source where the motion takes place in the four-dimensional Poincare translation sub-group of the BMS group.

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arXiv2005

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.

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arXiv1998

The Eikonal Equation in Flat Space: Null Surfaces and Their Singularities I

The level surfaces of solutions to the eikonal equation define null or characteristic surfaces. In this note we study, in Minkowski space, properties of these surfaces. In particular we are interested both in the singularities of these ``surfaces'' (which can in general self-intersect and be only piece-wise smooth) and in the decomposition of the null surfaces into a one parameter family of two-dimensional wavefronts which can also have self-intersections and singularities. We first review a beautiful method for constructing the general solution to the flat-space eikonal equation; it allows for solutions either from arbitrary Cauchy data or for time independent (stationary) solutions of the form S=t-S_{0}(x,y,z). We then apply this method to obtain global, asymptotically spherical, null surfaces that are associated with shearing ("bad") two-dimensional cuts of null infinity; the surfaces are defined from the normal rays to the cut. This is followed by a study of the caustics and singularities of these surfaces and those of their associated wavefronts. We then treat the same set of issues from an alternative point of view, namely from Arnold's theory of generating families. This treatment allows one to deal (parametrically) with the regions of self-intersection and non-smoothness of the null surfaces, regions which are difficult to treat otherwise. Finally we generalize the analysis of the singularities to families of solutions of the eikonal equation.

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arXiv1996

Fuzzy spacetime from a null-surface version of GR

The null-surface formulation of general relativity -- recently introduced -- provides novel tools for describing the gravitational field, as well as a fresh physical way of viewing it. The new formulation provides ``local'' observables corresponding to the coordinates of points --- which constitute the spacetime manifold --- in a {\em geometrically defined chart\/}, as well as non-local observables corresponding to lightcone cuts and lightcones. In the quantum theory, the spacetime point observables become operators and the spacetime manifold itself becomes ``quantized'', or ``fuzzy''. This novel view may shed light on some of the interpretational problems of a quantum theory of gravity. Indeed, as we discuss briefly, the null-surface formulation of general relativity provides (local) geometrical quantities --- the spacetime point observables --- which are candidates for the long-sought physical operators of the quantum theory.

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