It recently made the news that according to one new hypothesis about extra dimensions of space, miniature black holes could be common enough that there could be thousands in our solar system alone. However, I couldn’t find any answers to the following questions:
Are these mini-black holes different in conception from the standard black hole model? Are they based on an alternate theory of gravity or quantum physics? Or is it just being claimed that a mechanism exists for mini-black holes being created more abundantly than previoiusly thought? Would their properties be the same as Hawking black holes, or different somehow?
If mini-black holes exist in significant numbers within our solar system, wouldn’t they have been swept up by the Sun or Jupiter? Why do they think there might be many still in free orbits?
The paper by Keeton and Petters mentioned in ftg’s link is on the arXiv: parts IIIIII (links to abstracts). These papers are primarily interested in the observability of such small black holes via lensing effects. Large compact masses can be observed via static lensing effects (showing multiple images of compact objects behind them). Smaller masses can hopefully be observed by dynamic microlensing (by showing a characteristic change in the apparent luminosity of stars as they pass between the star and the observer). However, these black holes are so small that these techniques won’t work. Gould proposed using “femtolensing”: trying to detect interference fringes between the multiple paths around the lens. Keeton and Petters are extending this method to the smaller primordial black holes that appear in the Randall-Sundrum cosmology.
None of which answers your question, it’s just trying to link the news item to the literature. The black holes are different from the standard BH model, for the rather straightforward reason that the background spacetime is different (no longer a 3+1-dimensional spacetime, e.g.). Reference  from part III of K&P, by Guedens, Clancy, and Liddle, is the one that actually computes BH lifetimes in the RS cosmology. They find that in the RS spacetime, primordial black holes evaporate more slowly than modern ones; so the lower limit on primordial BH size is much smaller than in standard GR.
(Disclaimer: The above is from only cursory readings of the papers. I don’t know anything about branes.)
K&P part III makes the following statement:
(ref.  is to a pair of papers by J.D.Anderson, Astrophys. J., which are probably pre-arXiv, though I haven’t looked). I assume that the point is that the dissipative processes which allow large gas clouds to contract are not efficient at slowing dark matter (almost by definition) so that they tend to maintain their near-Keplerian orbits over cosmological time scales.
This in itself isn’t a big problem: After all, there are still plenty of asteroids, comets, etc. still in free orbits in the Solar System. The bigger problem would be that if even one black hole did get captured inside a large body, it ought to accrete from it, and eventually eat it away (and grow to easily-noticed mass, itself, in the process). I haven’t yet read the relevant papers, so I don’t know if they’ve addressed this.
There’s an object in the Cygnus X-1 system which, if it isn’t a black hole, would have to be something even weirder. Likewise for the object SagA*, near the center of our Galaxy. There’s never yet been a direct observation of a black hole itself, but the indirect evidence is pretty overwhelming.
“Reliably” is difficult to judge, but there is plenty of indirect observational evidence, based mainly on the expected emissions when matter falls into the hole. Cygnus X-1 was the first observed black hole; the interesting story of its discovery in the summer of 1972 is discussed here
Quite. I recall a seminar when some theorist posited that the so-called super-massive black holes, such as SagA* and larger that live at the centres of galaxies could be quark stars. He had to basically concede that there wasn’t really that much of a chance, since if they were quark stars, then things like radio galaxies couldn’t exist, as quark stars are posited to be quite unstable, and any accretion onto them will cause them to collapse into black holes.
I’m not sure about this - you can observe the accretion disc well enough, but to get inside the Schwartzshield radius will expose anything you could make for the observations to phenomenal tidal stresses. (Bad things happen when your head is accelerating at 8G, and your feet at 3G, even if they’re being accelerated along the same vector.)
The same way you observe anything black: You notice that you can’t see the things behind it. There’s some hope of getting this sort of observation for SagA* (the supermassive black hole at the core of the Galaxy), but it hasn’t happened yet.
(Bolding mine.) If you’re getting inside the Schwarzschild radius (which was what I was trying to imply) your CV has bigger problems than tidal stresses: you’re never coming out again, according to current understanding.
As for the tidal stresses near the Schwarzschild radius R, those depend on the size of the black hole. For large black holes the tidal stresses near R can be small, but you still can’t get back out again.
For the mini black holes being discussed in the OP, these tidal forces are large, but R is so small (they’d like to find black holes with masses <~ 10[sup]-19[/sup] M[sub]sun[/sub], thus having R <~ 0.3 fm: smaller than the radius of an atomic nucleus) that getting sufficiently close to the black hole to feel these forces is hard.
I understand that - what I’d meant to imply was that surviving to get inside the Schwarzchild radius requires passing through the zone where the tidal stresses will tear apart anything material that we can make. (Or so I understand the math.) The zone for any given black hole will vary with its mass and size, but all of them will have such a zone before anything material can pass beyond the Schwarzchild radius. So getting back out is a null factor, since before that you’ve been torn down to neutrons, protons and electrons.
(Yes, this is a debate on the order of talking about the number of angels dancing on the head of a pin…)
We might be disagreeing over a matter of terminology. “Tidal” forces usually refer to gravitational gradients, in my experience; for large black holes, the gravitational gradients near the Schwarzschild radius can be arbitrarily small. An observer falling freely into such a black hole won’t feel any large tidal forces (contrary to what you said)–but of course, he can’t get back out.
What grows large as you approach the Schwarzschild radius is the acceleration required to maintain “constant” position (or to escape back to infinity). This acceleration will also have some tidal components (inversely proportional to the distance to the horizon), but even large uniform acceleration (required to keep station near large black holes) will damage humans and instruments.