That is, if the closest one we can observe is 1600 light years away, are we not observing these things as they were 1600 years ago? How do we know black holes didn’t just pop up for a brief time window, and now they are gone?
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> That is, if the closest one we can observe is 1600 light years away
That’s the closest one that astronomers can observe “directly” (or at directly as you can ever observe a black hole). There is a supermassive black hole at the center of our own galaxy, but 1) there are a lot of stars and stuff between it and us, making that area hard to look at; and 2) it’s not actively feeding. It sucked up all the stuff that it could suck up millions or billions of years ago. Since black holes are, well…*black*, what astronomers want to observe is the *accretion disk* around the black hole, which is the gas and plasma and stuff that gets superheated as it rubs against itself swirling around the black hole. Our supermassive black hole (Sagittarius A*) does not have an accretion disk, so there’s not much to look at, there.
However, we *can* see the effects of that black hole. You can see in [this gif](https://cdn.vox-cdn.com/thumbor/HUPrAepWcueBotT0JPcAF-Qh7_I=/800×0/filters:no_upscale()/cdn.vox-cdn.com/uploads/chorus_asset/file/9984865/stars_orbit.gif) (found in [this article](https://www.vox.com/science-and-health/2018/1/8/16822272/black-hole-looks-like-what) how stars at the center of our galaxy are orbiting *something*. It’s marked in that gif, but in [this gif](https://cdn.vox-cdn.com/thumbor/a6tef_Av7GgpizrLek-PD0yhuZ0=/800×0/filters:no_upscale()/cdn.vox-cdn.com/uploads/chorus_asset/file/11759533/2018_07_26_11_40_29.gif) (from the same article) the “raw” images where there is nothing visible that the stars are orbiting. That something is, of course, the supermassive black hole Sagittarius A*.
So, the idea that we can’t observe black holes over time is somewhat flawed. We can’t *directly* observe a black hole ever – that’s kind of the point of a black hole. But there are plenty of ways to know that they’re there: observing the behavior of stars around them, detecting light from the accretion disk, detecting gravitational waves from black hole mergers, looking for [gravitational lensing](https://hubblesite.org/contents/media/images/2022/001/01FRKBDN5YKMM9ZMT5Q7TSN4RN)… Astronomers have detected black holes through all of these methods, and continue to observe them. Scientists at CERN **may** be able to create [microscopic black holes](https://angelsanddemons.web.cern.ch/faq/black-hole.html), although those would be extremely short-lived (fractions of a second).
Regardless, the ability to observe black holes is not required to predict their behavior. In fact, Einstein predicted the existence of black holes long before they were observed just by considering the implications of his theories of Relativity. Based on the mathematical equations, Einstein saw what could be possible. It wasn’t until decades later in 1971 that astronomers confirmed their existence. Based on those equations, Einstein made a number of predictions about their behavior. Stephen Hawking made even more predictions about black holes based on various equations of relativity and quantum mechanics. Those equations give scientists ideas about how black holes behave, and there’s really no way for a black hole to just *pop* into existence and then *pop* back out of existence. Hawking predicted that black holes could *slowly* evaporate through Hawking Radiation – losing energy and therefore mass until they eventually disappear. However, the time it takes depends on the size of the black hole. The larger the black hole is, the slower it evaporates. Stellar-mass black holes will take billions and billions of years. Supermassive black holes like Sag A* will take hundreds of billions, if not trillions of years.
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