A class of conformal curves in the Reissner-Nordstr\"om spacetime

TL;DR

This paper investigates a special class of conformal curves in Reissner-Nordström spacetime, demonstrating their smooth extension to infinity and analyzing conjugate points, with implications for conformal field equations and black hole simulations.

Contribution

It introduces a new class of conformal curves with prescribed initial data that extend smoothly to null infinity in Reissner-Nordström spacetime.

Findings

Conformal curves can be prescribed to extend smoothly to null infinity.

The formation of conjugate points on these curves is analyzed.

Results are relevant for conformal field equations and numerical black hole studies.

Abstract

A class of curves with special conformal properties (conformal curves) is studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data for the conformal curves can be prescribed so that the resulting congruence of curves extends smoothly to future and past null infinity. The formation of conjugate points on these congruences is examined. The results of this analysis are expected to be of relevance for the discussion of the Reissner-Nordstr\"om spacetime as a solution to the conformal field equations and for the global numerical evaluation of static black hole spacetimes.