If there really is a primordial black hole beyond the Kuiper belt, we can send a probe to the black hole and into it. But how fast must the probe be in order to enter the black hole without being ripped apart by spaghettification? The black hole in question has an event horizon diameter of 2-3 inches and 5-15 Earth masses so it is a tiny probe (tiny enough cameras do exist) we would have to launch. Let's say the probe is 1.5 inches broad and has a length of 2.5 inches. How fast must it be in order to not be torn apart and successfully enter the black hole?

  • $\begingroup$ What's the point of sending a probe into a black hole? Even if your probe survives for a few microseconds it cannot send any data back across the event horizon. $\endgroup$ – PM 2Ring Feb 13 '20 at 14:39
  • $\begingroup$ BTW, a black hole of that size has a mass around 4.5 Earth masses, and a test particle falls from the event horizon to the centre in about 0.2 nanoseconds. Its Hawking temperature is almost 4.6 millikelvin, with a luminosity of $4.9\times10^{-19}$ watts - not exactly easy to see. ;) $\endgroup$ – PM 2Ring Feb 13 '20 at 14:51
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    $\begingroup$ Also, for a distant observer who is not also falling to cross the event horizon, the probe takes infinite time to reach the event horizon. $\endgroup$ – notovny Feb 13 '20 at 14:53
  • $\begingroup$ @PM2Ring and notovny: First, we don't know what's in the center and if there is something like that at all. Second, there are uncountable reasons why we should send a probe to the black hole and also to try to send it into it. Third, we could send two probes: an orbiter and an impactor (similar to Cassini-Huygens) where the orbiter would observe from outside what the impactor looks like when falling into the black hole. $\endgroup$ – user30007 Feb 13 '20 at 15:12
  • $\begingroup$ Sure, we don't know if there's really a singularity at the centre of a BH - we need a quantum gravity theory to handle questions like that. Which is why I carefully said "centre" and not "singularity". ;) But standard GR is perfectly adequate to discuss what happens outside the event horizon, and it's also correct inside the event horizon, as long as you avoid the very centre of the BH. No light or other information (including gravitational signals) can come from inside the horizon, and a quantum gravity theory won't change that. $\endgroup$ – PM 2Ring Feb 13 '20 at 15:39

Let's try a crude back of the envelope calculation to get orders of magntitude:

The tidal force near the event horizon is of the order of $G M/r^3$ which is something like $10^{18} g/m$. So a probe with a mass of 1 gram and diameter of 1cm would experience about $10^{12} N$ of force trying to "spaghettify" it by accelerating ends of it at about $10^{16} g$ relative to the centre. If it experienced that force for a time $t$ the ends would likely move about $10^{17} t^2 m$ relative to the centre, assuming $t$ is short enough that relavity does not complicate things, so if we want to limit that to say 1mm we need $t < 10^{-10}$. So basically we want the probe to go from a few Schwarzchild radii down to 1 in about 100ps in its internal time frame, so that the tidal forces do not have time to tear it apart. Using the Newtonian approximation this is a few times faster than the speed of light, so what we learn is that the probe must be going at relativistic velocities, to have a chance of surviving. From its perspective, that flattens out the gravitational field around the black hole in the direction of travel, so that the tidal force seems to even briefer in duration.

  • $\begingroup$ Does it mean that there's no realistic chance to send a probe into the black hole without the probe being ripped apart? $\endgroup$ – user30007 Feb 13 '20 at 14:11
  • $\begingroup$ @user30007 What do you call realistic? You would somehow need to fire the probe in at quite close to light-speed, but there is no law of physics which says you can't do that. Also, how do you tell? Once the probe is inside the event horizon you will never hear from it again. $\endgroup$ – Steve Linton Feb 13 '20 at 16:06
  • $\begingroup$ You know what I mean. I said "no realistic", not "no possible chance". Even the Breakthrough Starshot probe doesn't go at 0.95c or something. But how can such a small black hole tear the probe so easily apart? I thought that about 11 miles/second (about the speed of Voyager 1) would be enough for the probe to survive. $\endgroup$ – user30007 Feb 13 '20 at 16:10
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    $\begingroup$ The smaller the black hole, the more intense the tidal forces. A 12 billion solar mass black hole with a radius of 35 billion km would have tidal forces around $10^{-12} gm^{-1}$. The gravity is strong but applies to the whole probe uniformly. For a tiny black hole, one end of the probe is much closer to the black hole than the other $\endgroup$ – Steve Linton Feb 13 '20 at 16:29
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    $\begingroup$ Whoa, black holes are not to be underestimated! $\endgroup$ – user30007 Feb 13 '20 at 18:46

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