B Cosmic expansion and shock waves

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TL;DR Summary
Do galaxies that have surpassed the speed of light during the cosmic inflation process emit radiation waves comparable to the sonic boom when an aeroplane breaches the sound barrier?
Do galaxies that have surpassed the speed of light during the cosmic expansion emit radiation waves comparable to the sonic boom when an aeroplane breaches the sound barrier?
 
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Adel Makram said:
TL;DR Summary: Do galaxies that have surpassed the speed of light during the cosmic inflation process emit radiation waves comparable to the sonic boom when an aeroplane breaches the sound barrier?
No. When space expands, there is no sense in which a galaxy has absolute motion. Locally, stars will emit light independent of the expansion of space. There's nothing happening locally to affect the emission of light.

Note that cosmic inflation took place in the very early universe when there were no stars of galaxies.
 
"Speed" is a slightly more slippery concept in curved spacetime than flat spacetime, and those galaxies aren't moving faster than light in the relevant sense.

Particles that exceed the speed of light in a medium emit Cerenkov radiation as they slow down.
 

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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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