Jonathan O’Callaghan in Quanta:
Identical twins have nothing on black holes. Twins may grow from the same genetic blueprints, but they can differ in a thousand ways — from temperament to hairstyle. Black holes, according to Albert Einstein’s theory of gravity, can have just three characteristics — mass, spin and charge. If those values are the same for any two black holes, it is impossible to discern one twin from the other. Black holes, they say, have no hair.
“In classical general relativity, they would be exactly identical,” said Paul Chesler, a theoretical physicist at Harvard University. “You can’t tell the difference.”
Yet scientists have begun to wonder if the “no-hair theorem” is strictly true. In 2012, a mathematician named Stefanos Aretakis — then at the University of Cambridge and now at the University of Toronto — suggested that some black holes might have instabilities on their event horizons. These instabilities would effectively give some regions of a black hole’s horizon a stronger gravitational pull than others. That would make otherwise identical black holes distinguishable.
More here.