The metric and curvature properties of
            <i>H</i>
            -space

Hansen, R. O.; Newman, Ezra T.; Penrose, Roger; Tod, K. P.

doi:10.1098/rspa.1978.0177

Cited by 85 publications

(55 citation statements)

References 6 publications

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“…Many years ago we studied [8,9] an unusual and remarkably simple formulaof the self-dual vacuum Einstein equations that turns out to be a special case of the present construction, Eq. (16).…”

Section: Self-dual Metricsmentioning

confidence: 99%

Einstein Equations via Null Surfaces

1994

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Section: Self-dual Metricsmentioning

confidence: 99%

Einstein Equations via Null Surfaces

1994

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“…This suggests that the same be done in general relativity (GR) to the center of mass so that the mass dipole vanishes. (2) It raises the question: can one generalize this transformation in GR and relate it to a remarkable property of regular shear free or asymptotically shear free null geodesic congruences (NGCs): that each such congruence is determined uniquely by a complex world-line in an auxiliary complex Minkowski space [6,3]?…”

Section: Complex Center Of Mass In An Asymptoticallymentioning

confidence: 99%

“…A most important technical tool for these calculations comes from an analysis of null geodesic congruences (NGCs) and specifically from the regular shear-free or asymptotically shear-free NGCs [5,6], all of which can be constructed from solutions of the so-called Good Cut equation [7]. The important point is the observation [2,3] that regular asymptotically shear-free null geodesic congruences in asymptotically flat space-times (or regular shear-free congruences in Minkowski space-time) are determined by the free choice of a complex worldline in an auxiliary complex Minkowski space-time: the freedom in the choice of solutions to the Good Cut equation.…”

Section: Introductionmentioning

confidence: 99%

Asymptotically stationary and static spacetimes and shear free null geodesic congruences

Adamo¹,

Newman²

2009

Class. Quantum Grav.

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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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“…4,5 In general it has a four complex dimensional solution space that has been dubbed H-space. H-space possesses a complex metric which is Ricci-flat with a self-dual Weyl tensor.…”

Section: A New Idea -Dynamics On I +mentioning

confidence: 99%

“…[Specifically and more surprising, it turns out to be a curve in H -Space. 4,5 ] At this point it is a completely arbitrary curve, i.e., any choice of the curve is related to the same shear. We show that there is a natural condition that can be imposed on the curve that makes it unique (up to initial data) that leads us to define the spin angular momentum and the center of mass from the real and imaginary parts of the complex curve.…”

Section: Introductionmentioning

confidence: 99%

Twisting null geodesic congruences, scri, H-space and spin-angular momentum

Kozameh

Newman

Silva-Ortigoza

2005

Class. Quantum Grav.

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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 spacetime 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.One should think of this work as developing a generalization of the properties of the algebraically special space-times in the sense that the term that is forced here to vanish, is automatically vanishing (among many other terms) for all the algebraically special metrics. This is demonstrated in one of several given examples. It was, in fact, an understanding of the algebraically special metrics and their associated shearfree null congruence that led us to this construction of the asymptotically shear-free congruences and the unique complex world-line.The Robinson-Trautman metrics and the Kerr and charged Kerr metrics with their properties are explicit examples of the construction given here.

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The metric and curvature properties of H -space

Cited by 85 publications

References 6 publications

Einstein Equations via Null Surfaces

Einstein Equations via Null Surfaces

Asymptotically stationary and static spacetimes and shear free null geodesic congruences

Twisting null geodesic congruences, scri, H-space and spin-angular momentum

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