Asymptotic Symmetries of the Null Infinity and the Isolated Horizon

TL;DR

This paper reviews the intrinsic geometry of null hypersurfaces and explores their asymptotic symmetries at null infinity and isolated horizons, revealing invariance under conformal transformations and classifying their infinitesimal symmetries.

Contribution

It introduces a unified analysis of the intrinsic geometry of null hypersurfaces and classifies their asymptotic symmetries at null infinity and isolated horizons.

Findings

Invariance of null hypersurface geometry under conformal transformations

Classification of infinitesimal symmetries of null hypersurfaces

Discussion of symmetries at null infinity and isolated horizons

Abstract

The common intrinsic geometry shared by all the null hypersurfaces gives rise to the asymptotic symmetries found on the null infinities $\mathscr I^\pm$ and the isolated horizons $\Delta$. In this work, the properties of a null hypersurface are reviewed and the invariance of its intrinsic geometry ($n^an^bh_{ab}$) is revealed under the spacetime conformal transformation. The generators, i.e., infinitesimal symmetries, of the conformal transformation tangent to the null hypersurface are defined and classified by their effects on the induced metric and the normal vector field. Two particular examples and their symmetries are discussed, that is, the null infinities $\mathscr I^\pm$ of an asymptotic flat spacetime, and the isolated horizon $\Delta$ of a black hole.