Equation 10 · The Atlas That Refuses to Close

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\Sigma

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a spacelike hypersurface and $u^\mu$ the four-velocity of the observer whose notion of simultaneity $\Sigma$ represents. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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\Sigma

Symbol Sigma

a spacelike hypersurface and $u^\mu$ the four-velocity of the observer whose notion of simultaneity $\Sigma$ represents.

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What the article says around this equation

Naming the slice is the first entry in this atlas’s notation. Let $\Sigma$ be a spacelike hypersurface and $u^\mu$ the four-velocity of the observer whose notion of simultaneity $\Sigma$ represents, with $\Sigma$ taken orthogonal to u . Replace the discrete sum with the body’s stress-energy tensor $T^{\alpha\beta}$ and define the energy centroid

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Sources cited in the article section

[14] General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles ↗

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