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Equation 31 · Part 9 · The Atlas That Refuses to Close

Denominator: Mc

ρM=∣S∣Mc.\rho_M = \frac{|\mathbf S|}{Mc}.
McMc

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

Mc occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The scale that answer is measured against is fixed entirely by the body itself. For a system of total mass M and spin angular momentum of magnitude |S\mathbf S| — the part of JμνJ^{\mu\nu} left over once the orbital piece is subtracted — define ρM=∣S∣Mc\rho_M = \frac{|\mathbf S|}{Mc}. ρM\rho_M has units of length by inspection, angular momentum divided by momentum, and it is built from nothing but the two Poincaré-invariant labels, mass and spin, that every observer agrees on regardless of which chart they read a position off of. It will turn out to be the radius of the region within which every well-behaved chart in this atlas has to stay.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.