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From what my non-scientifically-trained mind understands, matter typically enters a black hole via getting caught up in the accretion disc going faster and closer to the black hole until it passes the event horizon, the point of no return. Using Earth as an analogy for a black hole, I assume the accretion disc would orbit around the equator, similar to Saturn's rings, and the matter might eventually crash into Brazil or somewhere along the equator?

My main question is, can matter simply do a straight shot into the black hole at a higher latitude, say straight into New York City, avoiding the disc altogether?

As you can probably tell by my simplistic analogy, I am a complete layperson. While fancy jargon and artistic looking equations might be expected (which is fine), please also dumb it down to an average intelligent business administration major's level of scientific understanding.

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In your analogy: A satellite stays in orbit because it has angular momentum. This always balances the force of gravity, thus when being in the satellite (or in the ISS) it seems as if you're weightless, because force balance. This is very important to understand, because it is the reason that in space all orbital motions can -in principle- go on forever. Because angular momentum is conserved.

Now in order to crash into the Earth/BH you need to have very low angular momentum (which is equivalent to having only linear momentum straight down into the BH) or you have to loose the angular momentum somehow.
Near Earth, this happens to the ISS, because it has a low-earth-orbit between 350-450 km and at this height there are still enough atmospheric particles around to produce drag.

Around black holes it is a very similar thing.
I will define the Schwarzschild-radius $R_s = \frac{GM}{c^2}$ as a relevant length-scale. Then, as long as we are outside $3 R_s$ distance from the BH, we need, as on Earth, friction to dissipate our angular momentum. In the case of accretion discs that form around BH's this can be accomplished through turbulent dissipation as laid out in the famous paper by Shakura and Sunyaev.

Then, only very close to the BH, namely at a distance $< 3R_s$, space-time distortions help us to fall into the BH without the need for any additional source of friction. As you see, this is a region very close to the Black Hole and it is misrepresented in popular accounts of BHs that all matter orbiting it will magically fall into it.

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  • $\begingroup$ Thank you for your answer. I'm still confused if you're saying if it's possible or not. Can I shoot a proverbial bullet straight down, no angles, at the black hole's New York City and hit it? $\endgroup$ – iMerchant Feb 12 '17 at 23:30
  • $\begingroup$ Yes you can, if you aim well. The point of my answer was that usually in space this won't happen, and so infalling matter in general needs friction, before the BH can take over and 'devour' it. This is why in nature you usually have the disc. $\endgroup$ – AtmosphericPrisonEscape Feb 13 '17 at 1:53
  • $\begingroup$ Why a disc and not an accretion orb? I never understood why things in a 3D space (solar systems, planetary rings, etc) tend to more or less end up on the same ecliptic plane. Perhaps that's a different question altogether but somewhat related as my "bullet" is coming in at a different angle than the accretion disc. $\endgroup$ – iMerchant Feb 13 '17 at 3:20
  • $\begingroup$ Is it because BHs, stars, planets, etc spin on their axis so they aren't perfect spheres and bulge a little at their equators due to centrifugal force, thus having a greater gravitational force in the middle around the equator? Maybe I just answered my own question by thinking about it logically. $\endgroup$ – iMerchant Feb 13 '17 at 3:52
  • $\begingroup$ @iMerchant: Not sure if I'm understanding your question correctly, but it sounds like something that confused me alot as undergrad: How can a spherically symmetric blob of mass collapse into a disc? That wouldn't make alot of sense. Well the solution is that in reality nothing is perfectly spherically symmetric. Small asymmetries will amplify as the gas cloud collapses radially and will define a direction of net rotation for the whole cloud. After that it's just a matter of friction to bring the matter to the mid-plane of the future disc. It has nothing to do with greater grav forces. $\endgroup$ – AtmosphericPrisonEscape Feb 13 '17 at 15:03
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I suppose its certainly possible, however it's highly unlikely. First of all, you'd need your matter to fall in directly, meaning it would have to be traveling directly at the BH. Any motion slightly to the side, and it will start orbiting and spiral into the black hole. That's a pretty small target so that would already make this scenario not very plausible.

However, your main problem is going to be the fact that (1) black holes have magnetic fields usually and (2) black holes also usually spin. What this means is that anything trying to get into the black hole will tend to get swept up and taken along with the rotating magnetic field, causing it to start spiraling in. You could of course say that your infalling material is neutral and thus doesn't interact with the field, but there's no way it will stay neutral all the way in. At some point friction from falling in will make it a plasma and it will then be "bound" to the magnetic field. If you're knowledgeable about your magnetic fields, you may suggest making it so this matter could simply fall into the magnetic poles as it wouldn't then wouldn't be subjected to being dragged by the magnetic field. Unfortunately, the poles tend to be the regions where material escapes from the BH so you're unlikely to get infalling material through that.

In short, it might be possible to contrive some scenario where matter is just "dropped" onto the black hole but the circumstances for such an event to occur are exceedingly rare and will likely be ruined if the black hole is either spinning or has a magnetic field (which almost all do).

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    $\begingroup$ Not sure about the bit on becoming a plasma. There's not much friction, unless you interact with the accretion disc. Around a stellar black hole, tidal forces may be enough to rip you into a plasma (?) but tidal forces at the event horizon of a supermassive black hole are not very high. $\endgroup$ – James K Feb 13 '17 at 21:16
  • $\begingroup$ @JamesK I'm not sure either, but I anticipate it is certainly possible. My supposition is that the infalling material will become turbulent and potentially heat up enough to ionize. Even if it isn't a fully fledged plasma, some ionization might be enough to cause the effects I was talking about, especially of the material is dense enough that the ionized and unionized material can't decouple. I think any remarks on this topic will be speculative at best without full N body simulations or something. $\endgroup$ – zephyr Feb 13 '17 at 21:20
  • $\begingroup$ @JamesK: I think the disc should usually produce a nice amount of X and UV emission, for BH of a few solar masses. Depending on the efficiency of accretion, this can be up to a percent fraction of the Eddington luminosity. This will be enough to ionize anything that's incoming and not in the midplane of the accretion disc. $\endgroup$ – AtmosphericPrisonEscape Feb 15 '17 at 10:56

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