Recently, I stumbled across some writings such as https://link.springer.com/article/10.12942/lrr-2012-7 in which stationary black holes and their properties are discussed. However, before we theorize too much about these, I think one must look at if these are even realistic. Firstly, black holes are going to experience gravitational attractions, to say other larger, supermassive black holes. Secondly, anything that enters the black hole must have some motion and momentum going into the black hole, so in order for momentum to be conserved the black hole must accept the new objects' momentum, even creating the slightest of motion for a black hole. Finally, in what I think is the most definitive case against any possible black hole, is a black hole's origins. Black holes, typically, form because of the explosion of a supernova. This explosion obviously must come with some momentum (mass and velocity), which must be conserved in the formation and creation of a black hole. Hence, the black hole will then have some momentum and therefore motion, which to me really rules out the possibility of a stationary black hole.
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