Starting index or lower bound: Sigma

The passage around this formula

$X^\mu(u,\Sigma)$ 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.

Read this part in the article →