Does a non rotating BH have an accretion disc?
An idealised non rotating black hole would be an unlikely occurance, since black holes are formed from objects which do have angular momentum.
It's impossible to observe black holes, but it is possible to observe accretion disks which are outside of the event horizon.
Accretion disks seem commonplace, but there are also cases where no disk is apparent.
The black hole along with perturbation caused by other massive objects has probably resulted in all nearby matter falling into the hole and nothing significant remaining in the vacinity of the black hole.
I believe Sagittarius A*, the supermassive black hole at the center of our galaxy, has no prominent or permanent accretion disk. Sag A* was originally inferred to exist because stars were orbiting it in orbits that required a very compact, massive object. See also: http://en.wikipedia.org/wiki/Sagittarius_A*#Discovery_of_G2_gas_cloud_on_an_accretion_course
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