论文标题
几乎是kähler指标和PP波段的时间
Almost Kähler metrics and pp-wave spacetimes
论文作者
论文摘要
一方面，我们在一类严格的Kähler指标与Lorentzian PP-Wave SpaceTimes之间建立了一对一的对应关系；后一个指标在一般相对论中是众所周知的，它们在光速下建模辐射。具体而言，我们通过通过其传播波向量变形PP波来构建完全几乎Kähler指标的家族。我们获得的几乎kähler指标都存在于所有维度$ 2N \ geq 4 $，并且在$ \ mathbb {r}^{2n} $和$ \ Mathbb {s}^1 \ times \ times \ Mathbb {s}^s}^1 \ times m $中，几乎任何封闭的;它们不是扭曲的产品，它们包括具有恒定负标态曲率的非划合示例，并且所有这些都具有与Lorentzian PP-Wave指标共同关闭其基本2形式的特性。 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 $2n \geq 4$, every Lorentzian metric admits, locally, an almost Kähler metric of this form as a limit.
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 $2n \geq 4$, and are defined on both $\mathbb{R}^{2n}$ and $\mathbb{S}^1\times\mathbb{S}^1 \times M$, 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 $2n \geq 4$, every Lorentzian metric admits, locally, an almost Kähler metric of this form as a limit.
