$$(u,\Sigma)$$

Why this formula appears here

$X^\mu(u,\Sigma)$ is this article’s first chart. It takes two pieces of auxiliary data, an observer and a slice, and returns a point. Different choices of (u,$\Sigma$) for the identical physical body — the identical $T^{\alpha\beta}$ field, the identical total four-momentum $P^\mu$ = $\int_\Sigma$ $T^{\mu\nu}$\, d$\Sigma_\nu$ and total angular momentum $J^{\mu\nu}$ — can and do return different points, and the question this article is built to answer precisely is how different, and under what conditions the difference means something rather than nothing.

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