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The famous "No-Hair Conjecture" states that a blackhole can have only 3 hairs: Mass, Angular Momentum, and Electric Charge. It occurred to me that the basic underlying reason behind this might be that the interior of a blackhole can't causally influence the exterior. For the interior to not affect the exterior, it appears to be a necessary condition that the observations made in the exterior should only depend on the conserved quantities of the interior. Otherwise, a cosmohiker who has passed the horizon may change a non-conserved quantity (say, the number of particles) and (through the dependence of exterior observations on this quantity) send a message to the exterior. But no matter what he does, a conserved quantity is not going to change and thus, the exterior observations can possibly depend on only such conserved quantities.

I realize that it just puts an upper limit on how many hairs the blackhole can have and there certainly is a greater number of conserved quantities than the three included in the "No-Hair Conjecture" and the rest of them are not considered as hairs of the blackhole, e.g., the baryon number. So, this reasoning can not explain the whole picture but can a reasoning based on the causal arguments explain the rest of the picture? More importantly, is this reasoning appropriate at least for what it seems to explain (that a hair of a blckhole must be a conserved quantity)? Also, if the blackhole hairs are related to conservation laws then one should be able to relate them to symmetries. Is there any such interesting link that is known?