This is definitely fringe physics but here goes anyway.
Our physical theories are time reversible at the fundamental level.
We understand solutions to the GR equations for stuff falling into a black hole.
The time reversal of these solutions depict stars and even pink elephants springing out of black holes.
The solutions can be combined so that both are happening at once.
Do these solutions have any physical significance?
Some have written about “white holes” as the time reversed black hole but without much consideration of ramifications.
I know absolutely no way to predict what sort of stuff we should expect to emerge from a white hole, nor how much nor even how it scales with BH size.
Analytic extensions of the Schwartzschield or Kerr solutions indicate that there are two singularities; one at the sink for the in-falling stuff, and the other at the source of any emerging, new stuff.
These two singularities are separated from each other except perhaps for a momentary confluence as a black hole is created.
After that the only world lines between the two only carry signals from the source to the sink.
This means that whatever comes out may depend somehow on how the hole was formed, but not upon what subsequently falls in.
It might, however, depend on the three parameters of the black hole which numbers involve either singularity.
I can suggest no scaling law, however.
Someone has suggested as a physics rule of thumb, whatever can happen, must.
2006 Note
I wrote the stuff outside this paragraph about 2004.
I am now reading Lockwood’s “Labyrinth of Time” and am thereby convinced that stuff coming out of black holes is as unlikely as the air molecules in a room congregating under the table.
It is an entropy thing.
It would be possible but only thru incoming gravitational signals exquisitely phased to give form to the new stuff.
Not bloody likely!
This is the advanced gravitational potential idea.
Its time reversal corollary is that what falls into a black hole causes gravitational signals to be emitted that retain the information of what fell in.
There are famous controversies on whether black holes are information sinks.
I am impressed with Penrose’s concept of gravitational entropy as described by Lockwood.
All of this is incompatible with the rest of this page.
This is fringe stuff!
The Fringe Idea
The fringe idea is that dark matter springs from a black hole.
The idea does not suggest how much.
It does suggest that the amount of dark matter is increasing with time, especially in galaxies with major BH’s.
This may be testable some time.
These speculations require invoking unknown extensions of two successful but incompatible theories, GR and QM.
Combining incompatible theories is likely to predict nonsense.
Information Theory
I see no way to solve the problem of conservation of information with this idea.
Higgs Field
Warning: All I know of the Higgs field is what I have seen in the Scientific American!
There is a suggestion that very early in the big bang symmetry was broken and the Higgs field was frozen at some value that causes particular masses for elementary particles.
When a black hole forms the source singularity is formed at a time and place where the Higgs field intensity available.
This might make BH output more like normal matter than in a universe with a different Higgs field.
(I always preferred the explanation that all electrons weighed the same because there was just one of them.
In this perspective it still unclear how new stuff depends on formation of the BH.)
Hawking Radiation
Perhaps this is identical to Hawking radiation.
Hawking radiation comes with specific predicted intensities.
I think, however, that the predicted Hawking radiation is too little to account for the suspected dark matter.
(If I am not mistaken Hawking radiation can produce exotic matter with non-zero rest mass; since virtual particle pair creation happens for positive rest mass particles as well as photons.)
Combining Mysteries
It is tempting to match mysteries, using each to help explain the other.
Very occasionally this leads to useful insights but I think history is not kind to this sort of practice.
This idea is in that category by combining the nature of dark matter and the meaning of time reversed accreting BH solutions.