Primordial Black Holes mass diference with isomass stellar black holes How can we distinguish, for a given mass (measured from gravitational waves experiments and or other experiments) of a black hole or black hole binary, if they are PRIMORDIAL or they are stellar black holes or any other weird origin?
 A: That is very difficult. A black hole time dilates and redshifts radiation emitted by objects so it becomes virtually impossible to detect. As a result a black hole formed in the big bang and one formed by stellar collapse appear indistinguishable. The classical idea of a black hole is that it has “no hair,” which is to say there are no features other than mass, angular momentum and charge that defines the black hole. There is no additional “hair” on the horizon that distinguishes one black hole from another. 
I have written an essay for the FQXi contest on detecting quantum hair on black holes in the gravitational wave signature generated by the coalescence of two black holes. The classical gravitational field acts as a form of Heisenberg microscope that amplifies quantum hair on the horizon. The condition of this collision provide the conditions so these signatures are propagated in gravitational radiation. I leave the detailed reading up to the reader's interest in reading my paper. There is also a supplementary segment for mathematical details. Unfortunately this is fairly complicated and mathematical. It also involves some of the mathematics of Maryam Mirzakhani in her work on geodesics on hyperbolic spaces. The near horizon condition of a black hole is $AdS_2\times \mathbb S^2$ and this leads to some of this analysis with hyperbolic geometries. 
This will mean black holes have in their quantum details a large amount of information. It might then be possible to distinguish black holes formed by stellar collapse and putative primordial black holes. This is only possible under black hole coalescence. I am not sure though about what would happen if a primordial black hole and one formed by stellar collapse merge.
This is somewhat conjectural and I suspect there are those who will down vote it.
LC
