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There are a lot of questions about a small BH and the Earth, none of these answer my question specifically. And there are contradictory answers. Some of them state that the effects would be negligible, since the small BH could only eat very little. Others state that the effects would destroy Earth. My question is about the miniature BH passing through Earth at relativistic speed,and whether the Earth would stay in one piece.

I have read these questions:

What would the effect be of a small black hole colliding with the earth?

However, the gravitational effects from the black hole would be catastrophic.

If the moon became a black hole, how much would it eat in a day?

For example, if you got within a kilometer of this millimeter-sized thing your body would be torn apart by tidal forces. This is not what most people think of as completely normal.

How fast a (relatively) small black hole will consume the Earth?

If we take that at face value, it would take something like $10^{23}$ years for the BH to accrete $10^{24}kg$. If we factor in the change in radius of the BH, that time is probably much smaller, but even then it would be something much larger than the age of the universe.

What would happen if somebody dropped a small black hole into the Earth?

If the black hole is sufficiently light (much lighter than the Earth), it will tear a decent hole into the Earth, sink into its core (slowed down by the "accretion friction"), and may live there for a prolonged time accreting at the BHL rate before triggering some sort of instability in Earth's structure.

Now my question involves the relativistic speed.

There are a few factors to consider:

  1. The BH would eat very little in such a short time, since the interaction is very fast because of the relativistic speed.

  2. Anything that gets in the way of the singularity (anything that the singularity passes through), stays in there forever.

  3. Because of the relativistic speed, the (stress) energy of the BH would be enormous, its gravitational effects would pull Earth with it, and the tidal forces would tear Earth apart.

  4. The BH would just drill a hole through the Earth (because of the short interaction), or it would destroy it (enormous stress-energy).

Like when you shoot a bullet through glass, it just makes a hole, because of its speed, but the glass stays intact, so the Earth would stay intact too, or the energy of the BH would actually tear the Earth apart.

Just to clarify, the mass of the BH should be the mass of the moon, and it should come to a size of 1mm, that is the radius (EH).

For consideration, we can treat the Earth as a gravitational cloud of dust, if that is easier to model.

Question:

  1. What would happen if a miniature black hole (or a PBH) would pass through Earth at relativistic speed?
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  • $\begingroup$ there are contradictory answers There is no way in PSE to avoid this, and no guarantee that any answer is correct. So why ask the same question yet again? $\endgroup$ – G. Smith Jul 28 '20 at 17:42
  • $\begingroup$ I have voted to close as vague. You need to be clear about the mass of the hole. There is a vast range of “miniature” holes. $\endgroup$ – G. Smith Jul 28 '20 at 17:47
  • $\begingroup$ @G.Smith thank you, the mass is the moon, and it should come about 1mm (EH) radius, but I will edit to clarify. $\endgroup$ – Árpád Szendrei Jul 28 '20 at 19:32
  • $\begingroup$ @G.Smith the other questions, answers do not deal with relativistic speed BHs at all, especially when they pass through Earth. $\endgroup$ – Árpád Szendrei Jul 28 '20 at 19:33
  • $\begingroup$ OK, I’ve retracted my close vote. $\endgroup$ – G. Smith Jul 28 '20 at 19:35
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Quotes from a review of a theoretical paper dealing with :

What Would Happen if a Small Black Hole Hit the Earth?

But what if the black hole is small, perhaps a left over remnant from the Big Bang, passing unnoticed through our neighborhood, having no observable impact on local space? What if this small singularity falls in the path of Earths orbit and hits our planet?

...

So, picture the scene. The Earth (any planet for that matter) is happily orbiting the Sun. A small primordial black hole just happens to be passing through our solar system, and across Earths orbit. We are all aware of how a rocky body such as a Near Earth Asteroid would affect the Earth if it hit us, but what would happen if a small Near Earth Black Hole hit us? Theoretical physicists from the Budker Institute of Nuclear Physics in Russia, and the INTEGRAL Science Data Center in Switzerland, have been pondering this same question, and in a new paper they calculate how we might observe the event should it happen (just in case we didn’t know we had hit something!).

.....

This may be one tiny black hole, but it packs quite a punch. But is it measurable? PBHs are theorized to zip straight through matter as if it wasn’t there, but it will leave a mark. As the tiny entity flies through the Earth at a supersonic velocity, it will pump out radiation in the form of electrons and positrons. The total energy created by a PBH roughly equals the energy produced by the detonation of one tonne of TNT, but this energy is the total energy it deposits along its path through the Earths diameter, not the energy it produces on impact. So don’t expect a magnificent explosion, we’d be lucky to see a spark as it hits

.....

Any hopes of detecting such a small black hole impact are slim, as the seismic waves generated would be negligible. In fact, the only evidence of a black hole of this size passing through the planet will be the radiation damage along the microscopic tunnel passing from one side of the Earth to the other. As boldly stated by the Russian/Swiss team:t creates a long tube of heavily radiative damaged material, which should stay recognizable for geological time.” –

The orginal paper .

From the calculations whether it is relativistic speed or not might affect how much damage will happen on the PBH path , the slower the more . The path would be be a bit like the ionisation seen in bubble chamber pictures, where slow charge particles ionize a lot while relativistic ones ionise a minimum. It is all a matter of statistical encounters.

The review talks of a mass the size of a small mountain, and I see you want the size of the moon. One would have to go to the original paper and redo the calculations for a larger mass.

There is also this paper

From a review

Based on their calculations, VanDevender and his father, J. Pace VanDevender of Sandia National Laboratories in Albuquerque, New Mexico, estimate that one or two of these mini black holes passes through Earth every day.

....

By contrast, the event horizon for a mini black hole is smaller even than the diameter of an atom. This means that a mini black hole can zip through an entire planet and still have very little chance of veering close enough to an atom for it to pass the event horizon.

When a mini black hole does attract a particle, it will most likely circle the black hole far from the event horizon and not be absorbed, the theory states.

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  • $\begingroup$ Thank you so much! $\endgroup$ – Árpád Szendrei Jul 29 '20 at 15:54

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