#
APS April Meeting 2011

## Volume 56, Number 4

##
Saturday–Tuesday, April 30–May 3 2011;
Anaheim, California

### Session X4: Einstein Prize and New Methods for Old Problems in Gravitational Physics

10:45 AM–12:33 PM,
Tuesday, May 3, 2011

Room: Garden 4

Sponsoring
Unit:
GGR

Chair: Patrick Brady, University of Wisconsin-Milwaukee

Abstract ID: BAPS.2011.APR.X4.1

### Abstract: X4.00001 : Einstein Prize Talk: Light-Cones in Relativity: Real, Complex and Virtual - with Applications

10:45 AM–11:21 AM

Preview Abstract
Abstract

####
Author:

Ezra T. Newman

(University of Pittsburgh)

We present some observations about certain unusual geometric
structures that appear in both Minkowski space and asymptotically
flat space-times. Three different types of light-cones are
considered: ordinary real light-cones in Minkowski space, M,
complex light-cones in the complexified Minkowski space,
M$_{C}$,(Minkowski coordinates x$^{a}$ go to complex z$^{a}$) and
third, virtual light-cones in asymptotically flat space-times.
All three types are defined at future null infinity, I$^+$,
(I$^+$ defined by the endpoints of infinite extensions of future
directed null geodesics) via the vanishing of the shear of the
null geodesics lying in the null surface. The virtual light-cones
appear to converge to points in an auxiliary virtual space,
H-space. Cones are labeled by their apex coordinate x$^{a}$ or
z$^{a}$. Two applications are discussed. The first begins with
asymptotically flat Maxwell fields written as W=E+iB. On each
light cone, with apex x$^{a}$, extracting the l=1 harmonic of the
Maxwell field determines the complex electromagnetic dipole
moment, D$_{E\&M}=$D$_{E}+iD_{M}$. D$_{E\&M}$, a function of
x$^{a}$, can be analytically extending into M$_{C}$. Its zero
set, points in M$_{C}$ where D$_{E\&M}$(z$^{a}$) vanishes, is a
complex curve called the complex center of charge world-line. The
second application virtually repeats the Maxwell case but now for
asymptotically flat Einstein/Einstein-Maxwell fields. In the
asymptotic region of each virtual light-cone, extracting the l=1
harmonics from the asymptotic gravitational field (the Weyl
tensor) yields the complex gravitational dipole,
D$_{Grav}=$D$_{Mass}+$iD$_{Spin}$. Each cone is labeled by its
H-space apex z$^{a}$. D$_{Grav}$(z$^{a}$) is thus a function on
H-space. Its zero set determines an H-space curve: the complex
center of mass world-line. Interior space-time physical
quantities and dynamics, (e.g. center of mass, spin, angular
momentum, linear momentum, force, eqs. of motion) are identified
at I$^+$ and described in terms of this complex world-line.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.APR.X4.1