Think of horizon as spherical membrane of thickness Lp.
So c/A^1/2 are the theta, phi phase waves in an effective order parameter potential V(r, theta, phi).
As A ---> infinity the frequency ---> 0 - massless Goldstone mode.
However, the Higgs mode I predict is in the radial vibrations peak frequency c/Lp gets red shifted by (Lp/A^1/2)^1/2 < 1 at the detector to peak frequency
c/(LpA^1/2)^1/2 > c/A^1/2
In limit A ---> infinity both modes are gapless, but as soon as A is finite the Higgsian type mode splits off a higher frequency branch.
Not sure how far this analogy goes, but I want to record it just in case.