While there is lots of evidence showing black holes exist, we’d really like to observe them more directly.
Eat and Run
A millisecond pulsar is a neutron star that is rotating about 600 to 700 times a second. Because of their strong magnetic fields, they produce strong beams of radio energy from the regions of their magnetic poles, and as they rotate these beams can point in our direction. As a result, we observe these neutron stars as radio bursts that pulse every 1 – 10 milliseconds. Hence their name.
Animal Magnetism
One of the challenges to understanding black holes is that when things get close to a black hole, things get complicated. We actually have a good description of black holes by themselves, but the description of the heated material near a black hole is complex. To understand the behavior of this material you need to account for not only the gravitational attraction of the black hole, but also things such as magnetic fields. To model active black holes, you need sophisticated computer simulations, and those simulations rely on certain assumptions about how black holes interact.