Not so, only one of the two solutions is unstable: https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Circul...

Also, this applies only to circular orbits, and does not indicate that a powered ship could not maintain orbit.

Those orbits are all outside the event horizon. Inside it, all you can hope to do is fall inward as slowly as possible.

BTW most of what I know about black hole physics is from Greg Egan's novel "Incandescence". Which covers quite a lot of science for a work of fiction (and overall extremely inspiring).

http://gregegan.customer.netspace.net.au/INCANDESCENCE/Incan...