Black Hole system with planets?

There is no such thing as stupid questions, just stupid people (like me).

Lets say that there is a binary system comprising of a stellar black hole and a solar main sequence star. Both orbit each other in a fairly circular orbit that makes them about 100 AU away from each other. Could planets (let alone habitable planets or life) exist around the solar twin star?

At that distance the funky relativistic effects of the black hole can be ignored, so stability-wise I don't see there'd be a problem.

Formation issues are more tricky. If the configuration is primordial then the solar-type star would have formed in extreme proximity to an O-type star (the supernova progenitor), an environment which is observed to be unhealthy for the survival of protoplanetary discs at distances of several light years let alone at bound orbit distances. (And that is before the supernova gets to wreak havoc with the place).

On the other hand if the black hole is captured into orbit (perhaps exchanging with a pre-existing companion to the solar-type star), things seem more hopeful. However assuming the captured black hole's orbit is randomly oriented with respect to the plane of the solar type star's planetary system, in roughly 3/4 (IIRC) of the cases you get Kozai oscillations which can seriously mess up a multi-planet system, even if the post-capture orbit has a periastron sufficiently distant to avoid directly disrupting the planets.

Whether you'd get a near-circular orbit for a wide black hole+solar type star binary is also questionable. Neither capture nor a post-supernova system seem particularly likely to give you this.

Does the Kozai mechanism always result in higher eccentricities? Could it be that an Earth-mass planet outside the habitable zone, is forced into it via the Kozai mechanism?

I don't know much about Kozai oscillations...

Mechanical issues apart , it seems to me that the solar wind and remains of the protoplanetary disk as dust , or even asteroids/comets would provide an unhealty dose of x/gamma rays to any nearby planet as they colapse into the black hole.
If the main secuence star , the planet and the black hole are coplanar , then , anytime the planet goes between the star and the black hole , an insane amount of solar wind may colapse any van allen structures the magnestosphere could make. The push from the star and the pull from the black hole may create a "corridor" of very fast-moving plasma. Not sure if that would have any measurable effect in the planet's orbit , but sure it would make a dent in any living creature not shielded by a healthy layer of rocks or water.

Not sure if that would be an asset or a liability to evolution , but sure it would make a bumpy ride for life

Listen to an episode of Astronomy Cast, they said no.

Due to the accretion disk and the high blast of radiation, it will be hard for matter to condense as well as the turbulant movement of particles and gravity.

So no.

But, far away enough from the black hole, not sure on that. Astronomy Cast did not mention how far you could be.

Did they consider a capture scenario?

Don't remember. It was one of the answer & question episode. One of the recent ones.

it was my understanding that capture scenarios generally do not create circular orbits. thus the star, or black hole on elliptical path through the system would create instabilities in any planetary formations.

i wouldn't be surprised if any planet forming material were stripped away from the star, either falling into the black hole or being ejected from the system, and then the star itself slowly stripped apart and destroyed.