Twistors and the asymptotic behaviour of massless spin- fields

Abstract

Abstract. In this work the asymptotic solutions of massless spin-3 2 fields are studied. First, in a Minkowski space, the fields, their potentials, and the associated gauges are analysed in the Rarita-Schwinger description. We exhibit the explicit appearance of the conserved charges of the fields and their singular behaviour in the potentials. The charges of the spin-3 2 fields emerge as a global definition of twistors. The flat space case serves as a guide in the analysis of the problem in general vacuum spacetimes. Although the fundamental connection between and the meaning of twistors and charges have not, as yet, been established in general vacuum spacetimes, some useful insights have nevertheless been gained in studying the potential-modulo-gauge description of the spin-3 2 problem in such spacetimes.

Mode stability on the real axis

“…As discussed by Penrose (1965), an analysis of the asymptotic behavior of massless fields at null infinity leads, upon taking into account the scaling properties of the tetrad components of the field, to specific rates of fall-off depending on the spin weight of the field. This is known as the peeling property; see Mason and Nicolas (2012) ;Frauendiener, Ghosh, and Newman (1996) (2) we find for that the peeling behavior of the solution of the TME is…”

“…As discussed by Penrose (1965), an analysis of the asymptotic behavior of massless fields at null infinity leads, upon taking into account the scaling properties of the tetrad components of the field, to specific rates of fall-off depending on the spin weight of the field. This is known as the peeling property; see Mason and Nicolas (2012); Frauendiener, Ghosh, and Newman (1996); Andersson, Bäckdahl, and Joudioux (2014); Hinder, Wardell, and Bentivegna (2011) for discussions of various aspects of peeling. The peeling property can be summarized by saying that for a scalar component ϕ s of spin weight s, defined with respect to the Kinnersley tetrad, we have ϕ s = O(r −3−s ).…”

One-loop divergences in simple supergravity: Boundary effects

“…where ✷ AM ≡ ∇ B ′ (A ∇ B ′ M ) , and ✷ ≡ ∇ CF ′ ∇ CF ′ . Remarkably, if the following first-order equation holds [12,38,39,72]:…”

From Spinor Geometry to Complex General Relativity

“…It has been our aim to give a pedagogical introduction to twistor theory, with emphasis on the topics and methods that a general relativist is more familiar with. Much more material can be found, for example, in [18], especially spin-3/2 potentials ([1], [23], [47], [24], [25]) and various definitions of twistors in curved space-time [59]. Moreover we should acknowledge that complex (Riemannian) manifolds have been investigated from the point of view of the corresponding real structure in [8], [9].…”