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The phenomenon of electric current superconductivity is well known and there are even talks about color charge superconductivity.

Is there a context in which gravity superconductivity makes sense? It seems that all known bosons have gravitational attraction (even if they are massless) so we should expect all matter to be gravity superconducting. At the same time, all materials seem to be transparent to gravitational interaction so maybe it is superfluous, since normal conductivity happens in condensed (non-transparent) matter. The actual effect is expected to be very small before stellar scale.

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    $\begingroup$ How would you define a "gravitational current" in the first place? $\endgroup$
    – paulina
    Commented Aug 27 at 19:31
  • $\begingroup$ That's a great question as well! $\endgroup$
    – alamar
    Commented Aug 27 at 19:33
  • $\begingroup$ Apart from that, matter is not "transparent" to gravitational influence. I'm not sure if that even makes sense to say, since the presence of matter is what causes gravity in the first place. $\endgroup$
    – paulina
    Commented Aug 27 at 19:37
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    $\begingroup$ That's precisely what I am asking, is there some physical context where this concept has relevance. $\endgroup$
    – alamar
    Commented Aug 27 at 19:54
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    $\begingroup$ Superconductivity is a quantum effect, not a classical one, as far as I know. But there is no accepted theory of quantum gravity, so I don’t see how the question could be answered or be on-topic. $\endgroup$
    – Ghoster
    Commented Aug 27 at 19:54

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Superconductivity usually is a phenomenon associated with the Higgs mechanism:

Superconductivity of an interaction $\alpha$ in a medium arise when the medium spontaneously break the simmetry associated to the gauge boson carrying the interaction $\alpha$.

This happens for EM superconductors where the photons get a mass inside a superconductor (the Cooper pairs are responsible for the symmetry breaking).

This happens for the electroweak theory where the weak bosons get a mass inside the vacuum (this counts as a medium!) making the vacuum an electroweak superconductor (the Higgs is responsible for the symmetry breaking)

This happens also in QCD as you already posted.

For this to happen in gravity you need first to define gravity as a gauge theory: this is done classically via the use of Ashtekar variables.

Next you need a vacuum state of this theory and something to break the gauge symmetry of this vacuum: lacking a complete theory of quantum gravity, this part is yet unknown so a "gravitational superconductor" is for now not being studied, at least that i am aware of.

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