Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

TL;DR

This paper investigates how gravitational, electromagnetic, and spin fields behave asymptotically near conformal infinity in spacetimes with a cosmological constant, revealing a universal directional structure influenced by the Petrov type.

Contribution

It extends the understanding of the peeling-off property to spacetimes with non-zero cosmological constant, detailing the directional dependence of radiation near different types of conformal infinity.

Findings

Radiation vanishes along directions opposite to principal null directions for Lambda>0.

Directional dependence of fields is influenced by Petrov type and orientation of null directions.

Near anti-de Sitter infinity, the structure depends on the number and orientation of principal null directions.

Abstract

We analyze the directional properties of general gravitational, electromagnetic, and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of I. The standard peeling-off property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for Lambda>0) or timelike (for Lambda<0), and the radiative component of each field depends substantially on the null direction along which P is approached. The directional dependence of asymptotic fields near such de Sitter-like or anti-de Sitter-like I is explicitly found and described. We demonstrate that the corresponding directional structure of radiation has a universal character that is determined by the algebraic (Petrov) type of the field. In particular, when Lambda>0 the radiation vanishes only along directions which are opposite to principal null directions. For Lambda<0 the directional dependence is more complicated because it is necessary to distinguish outgoing and ingoing radiation. Near such anti-de Sitter-like conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to I. The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This offers a better understanding of the asymptotic behaviour of the fields near conformal infinity.