Equation 143 · Part 3 · The Entry a Relabeling Cannot Write
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
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…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.