On the conformal structure of the extremal Reissner-Nordstr\"om spacetime

TL;DR

This paper explores the conformal geometry of extremal Reissner-Nordström spacetime, providing regular representations near key infinities and horizons, with implications for field propagation and perturbations.

Contribution

It introduces conformal representations of neighborhoods near infinity and horizons that are regular with respect to conformal Einstein equations.

Findings

Conformal representations near spatial and null infinities are constructed.

These representations are regular with respect to Einstein field equations.

Implications for test field propagation and gravitational perturbations are discussed.

Abstract

We analyse various conformal properties of the extremal Reissner-Nordstr\"om spacetime. In particular, we obtain conformal representations of the neighbourhoods of spatial infinity, timelike infinity and the cylindrical end ---the so-called cylinders at spatial infinity and at the horizon, respectively--- which are regular with respect to the conformal Einstein field equations and their associated initial data sets. We discuss possible implications of these constructions for the propagation of test fields and non-linear perturbations of the gravitational field close to the horizon.