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Equation 31 · Part 1 · The Atlas That Refuses to Close

Symbol rho_M

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

What this part means

rhoMo_M is part of the quantity the equation computes from the expression on the right.

Its job in the formula

rhoMo_M is part of the quantity the equation computes from the expression on the right.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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