The peeling theorem with arbitrary cosmological constant

Abstract

A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the outstanding case of the physical Weyl tensor provides the explicit form of all terms that determine its asymptotic behaviour along arbitrary lightlike geodesics. The results follow under the assumption of a conformal completion à la Penrose. The only freedom available is the choice of a null vector at the conformal boundary of the space-time (which determines the lightlike geodesic arriving there).

Gravitational Radiation at Infinity with Non-Negative Cosmological Constant

“…The absence/presence of radiation on a cut may in general be due to a balance between several possible components, and this varies from one cut to another. This was somehow recognized time ago as a dependence of the radiative part of the field on the direction of approach to J if J is not a null hypersurface [62,49,30].This issue is of special importance when considering isolated sources of the radiation, or sources that are confined to a compact region of the spacetime, emitting gravitational radiation.…”