News tensor on null hypersurfaces

TL;DR

This paper introduces a geometric definition of the news tensor on null hypersurfaces, linking it to radiative components of the Weyl tensor and exploring differences at null infinity in four-dimensional spacetime.

Contribution

It provides a new geometric formulation of the news tensor and derives a generalized transport equation for the Geroch tensor, enhancing understanding of gravitational radiation.

Findings

Correct expression for radiative Weyl tensor components at null infinity

Generalized transport equation for Geroch tensor derived

Differences between bulk null hypersurfaces and null infinity discussed

Abstract

A geometric definition of news tensor on null hypersurfaces in four space-time dimensions is presented. When the conformal Einstein field equations hold, this news tensor yields the correct expression for the radiative components of the rescaled Weyl tensor at infinity with vanishing cosmological constant in arbitrary conformal gauge. Also, a generalised transport equation for the Geroch tensor is derived. Important differences between null hypersurfaces in the bulk of the space-time and null infinity with vanishing cosmological constant are reviewed, and their impact on the role of the news is discussed.