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I apologize in advance if this is a too basic question. Let $(M,g)$ be a Lorentzian manifold with signature convention $(-,+,\dots,+)$. Now, lets suppose $X\in\Gamma(TM)$ defines a global time-...

Let $(\mathcal{M},g)$ be a Lorentzian manifold, which is globally of the form $\mathcal{M}\cong I\times\Sigma$, where $I\subset\mathbb{R}$ ("time") and $\Sigma$ ("space") is some $...

For vector fields in $R^3$ one knows that there exists a unique decomposition of vector fields in to solenoidal (divergence free) and potential parts. A generalization of this Theorem for symmetric ...