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One of the things we tend to do in astronomy is assign different names to things that are basically the same. Take, for example, the term perihelion. The word derives from the Greek peri (close) and helios (Sun) and represents the point at which an orbiting body is closest to the Sun. If a body is orbiting the Earth, then the term is perigee, from geos (Earth). Following the Greek, you get other terms: periareion for Mars, periastron for a star, and so on. There’s also the general term periapsis, but the cool kids like to use specific terms. So what about the closest approach to a black hole? What’s become popular is peribothron, from bothros meaning hole or pit. You’ll likely see the term a bit more because we’re now able to observe bodies reaching peribothron around the black hole in the center of our galaxy. In particular, a body known as G2 has recently passed peribothron at a distance of only 36 light hours from the supermassive black hole, and we’ve imaged the event with the greatest resolution yet.
