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Equation 143 · Part 1 · The Entry a Relabeling Cannot Write

Symbol mu

∇μTμν=0\nabla_\mu T^{\mu\nu}=0
μ\mu

What this part means

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

Its job in the formula

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

The passage around this formula

Cosmology removes the Killing vector altogether rather than merely complicating it. The Friedmann-Lemaître-Robertson-Walker spacetime describing the large-scale universe has no timelike Killing vector in comoving coordinates: its metric depends explicitly on time through the scale factor, and no coordinate change removes that dependence globally. There is consequently no analog of the ADM or Bondi construction supplying a global conserved energy for, say, the universe’s total photon population. A single photon’s cosmological redshift is the precise observational face of that absence: its frequency, and with it its energy, decreases as the universe expands, and this is exactly what an absent…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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