Locally Conformally Flat Lorentzian Gradient Ricci Solitons

TL;DR

This paper classifies locally conformally flat Lorentzian gradient Ricci solitons, showing they are either Robertson-Walker warped products or plane waves, with the latter being necessarily steady, based on the gradient of the potential function.

Contribution

It provides a complete local classification of such solitons, linking geometric structures to the nature of the potential function's gradient.

Findings

Non null gradient leads to Robertson-Walker warped product structure.

Null gradient results in plane wave structure.

Plane wave solitons are necessarily steady.

Abstract

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily steady.