Conformal isometry of the six-dimensional black string and dualities of null geodesics

TL;DR

This paper demonstrates a conformal isometry in a six-dimensional black string and explores duality relations among null geodesics in different brane geometries, revealing geometric origins via optical metrics.

Contribution

It introduces a conformal isometry in six-dimensional black strings and uncovers dualities of null geodesics with geometric insights from optical metrics.

Findings

Conformal isometry under inversion for six-dimensional black string

Duality relations between null geodesics of brane geometries

Geometric origin of dualities through optical metrics

Abstract

We show that the extreme six-dimensional black string admits a conformal isometry under inversion. Duality relations between null geodesics of various brane geometries are demonstrated, some of which have a geometrical origin through an optical metric.