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

Abstract

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, I + C , 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 worldline; 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 infinty I + , (center of mass, spin, angular momentum, linear momentum, force) are given kinematic meaning and dynamical descriptions in terms of the complex world-line.

Transformations of asymptotic gravitational-wave data

“…With the algorithm presented in this paper, we can begin to investigate ways to achieve such alignment. Previous investigations have suggested ways of using asymptotic data to determine the center of mass, and more generally resolve the supertranslation ambiguity [33,[56][57][58]. While these are promising theoretical developments, additional work will be needed to make these methods practicable-towards which the present work is a crucial first step.…”

“…In principle at least, this approach could also be extended to the full BMS group, though the supertranslations would obviously be represented only up to some finite sphericalharmonic order, and the numerical implementation may be delicate. It may also be feasible to resolve the gauge ambiguities using any of various methods presented in the literature [33,[56][57][58], though it is not clear that such an approach would be numerically feasible. In any case, a simplistic approach like the one found in Sec.…”

Stringlike structures in Kerr-Schild geometry: The N=2 string, twistors, and the Calabi-Yau twofold

“…Complex world sheet of his string is embedded in the real Kerr geometry, and as it discussed in I, the real and complex Kerr strings form together a membrane, which is analogous of the enhancon model of the string/M-theory unification, [14]. Recently, the both Kerr strings were mentioned in [15] by Adamo and Newman, and they reaction is worth quoting: "...It would have been a cruel god to have layed down such a pretty scheme and not have it mean something deep. "…”

Струнные Структуры В Геометрии Керра - Шильда: ${N=2}$ Струна, Твисторы И Комплексно-Двумерное Многообразие Калаби - Яу

“…Комплексная мировая поверхность струны вкладывается в вещественную геометрию Керра, и, как обсуждалось в работе [1], вещественная и комплексная струны Керра вместе образуют мембрану, по аналогии с переходом от теории струн к M-теории [14]. Недавно обе струны Керра были упомянуты в работе [15], и, чтобы описать реакцию авторов, лучше всего привести цитату из этой работы: "... Бог должен оказаться довольно злонамеренным, чтобы составить такую красивую схему и не обеспечить, чтобы за ней было что-нибудь глубокое". В дополнение к этой струнной системе в работе [1] получен еще один замечательный факт -показано, что появляется комплексно-двумерное многообразие Калаби-Яу (поверхность K3) в проективном твисторном пространстве геометрии Керра.…”