"Almost Kähler metrics and pp-wave spacetimes" by Amir Babak Aazami and Robert Ream
 

Mathematics

Almost Kähler metrics and pp-wave spacetimes

Document Type

Article

Abstract

We establish a one-to-one correspondence between a class of strictly almost Kähler metrics on the one hand and Lorentzian pp-wave spacetimes on the other; the latter metrics are well known in general relativity, where they model radiation propagating at the speed of light. Specifically, we construct families of complete almost Kähler metrics by deforming pp-waves via their propagation wave vector. The almost Kähler metrics we obtain exist in all dimensions 2 n≥ 4 , and are defined on both R2n and S1× S1× M, where M is any closed almost Kähler manifold; they are not warped products, they include noncompact examples with constant negative scalar curvature, and all of them have the property that their fundamental 2-forms are also co-closed with respect to the Lorentzian pp-wave metric. Finally, we further deepen this relationship between almost Kähler and Lorentzian geometry by utilizing Penrose’s “plane wave limit,” by which every spacetime has, locally, a pp-wave metric as a limit: using Penrose’s construction, we show that in all dimensions 2 n≥ 4 , every Lorentzian metric admits, locally, an almost Kähler metric of this form as a limit.

Publication Title

Letters in Mathematical Physics

Publication Date

8-2022

Volume

112

Issue

4

ISSN

0377-9017

DOI

10.1007/s11005-022-01569-4

Keywords

Almost Kähler metrics, plane wave limit, pp-waves

Link to Full Text

Share

COinS