15 - A Two-surface Encoding of Radiative Space-times

Summary

Introduction

The purpose of this work it to represent an alternative approach or description of the geometry of asymptotically simple space-times [1]. The essential idea behind this approach is the attempt to analyze the gravitational field at any given interior point of a space-time using the imprint left at null infinity by light originating from that point. To be more specific, given a point x^μ and its future (or past) light cone N_x, the light cone cuts of null infinity are defined as C_x = N_x⋂I, where I, null infinity, is the null boundary attached to an asymptotically simple space-time [2]. One then shows that knowledge of the geometry of the cut C_x and the neighboring cuts, for an arbitrary point x^μ, is equivalent to knowledge of the conformal metric at that point [1]. (These cuts have actually been explicitly calculated and the conformal metrics reconstructed in the case of the Schwarzschild, Kerr and charged Kerr metrics [1].)

Though the goals of this formalism have been out lind elsewhere [3] one can say that the main areas of research in the program are: a) kinematical description of the cuts, b) dynamical description of the cuts, and c) quantum description of the cuts.

The main purpose of the present work is to present some new results concerning part a) of the program, though towards the end we will make comments on part b).