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Would it be a feasible scenario?

I have read this question:

What would happen to the Moon if Earth is turned into a black hole?

Where Lubos Motl says:

The extremal Kerr J=GM2/c∼RbhMc. Now, the Earth-mass black hole has radius 9 mm or so so we get about 1030 Js. The Earth's spin, actual angular momentum now, is indeed over 1040, ten orders of magnitude too much. This discrepancy is of course linked to Earth's too low density that makes the collapse de facto impossible.

So based on this, the moon needs a radius of 2 mm. So let's disregard that the moon's low density makes it practically impossible to collapse, but let's instead say that it already is a black hole, size 2 mm, and nothing else, changes, it is revolving around the Earth, same speed, trajectory.

  1. Would this be possible? Can a planet have a black hole moon at all?

  2. Would anything on Earth change?

Árpád Szendrei
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    The correct figure for the Schwarzschild radius of the Moon is about 0.11 mm, not 2 mm. – Dmitry Brant Oct 13 '18 at 19:39
  • @Dmitry Brant here op is taking about Kerr black hole whose event horizons are given by $r_{\pm}=GM\pm\sqrt{G^2M^2-\frac{J^2}{M^2}}$ where schwarzschild event horizon is given by $2GM$ therefore answer is of by a factor of 2. – aitfel Oct 13 '18 at 19:50
  • @David Z I specifically cited a reverse question, that was not put on hold, that was not too broad. – Árpád Szendrei Oct 14 '18 at 00:43
  • @ÁrpádSzendrei Sure; that's a different question. (It did kind of look like a duplicate, though, so I've marked it accordingly now.) – David Z Oct 14 '18 at 00:47

1 Answers1

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NOTHING.

The exoticness of black holes lies between their singularity and event horizon. Outside of this region we won't we able to tell whether it's a normal star or a black hole. Though there might be ways to detect the difference like gravitational lensing.

Take for example Schwarzschild space-time (for Kerr there may be added effect like frame dragging let's leave it for simplicity) and just analyse Kruskal diagram in region I (any one of the asymptotic flat space-time) you will get your answer.

Though there might be some effect of Hawking-radiation (if it really happens in nature) like observing black hole radiation it will be then quite easy for us to experimentally verify it. Also the existence of black hole in nature can also be then verified as this black hole will be quite close to us though it's tiny size may cause some detection complication.

But if one starts to think what initial condition are to given to the initially exploding star, of which Earth and moon or as a matter of fact our whole solar system is a child, so that only the moon became a black hole but Earth doesn't it seems quite improbable though one has to do simulation to verify it.

Also this is one of the question which is put forward as a caution in almost all friendly GR books (for ex. Sean) to break the myth that black holes are like suction pump ready to suck everything inside it however far the object feeling gravity due to it is, the way it is depicted in sci-fi movies

aitfel
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  • Would not most radiation come from an accretion disk? –  Oct 13 '18 at 20:11
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    Re, "exoticness of black holes lies between their singularity and event horizon," Yes, but there's a region outside the event horizon where the strong spacetime curvature would make it a not-fun place to visit (e.g., as in Larry Niven's short story, "Neutron Star – Solomon Slow Oct 13 '18 at 21:20
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    There would be no moonlight ever, which is not my idea of no change. We would not even be aware of the Moon's existence and it would likely have to be inferred from other evidence (e.g. tides), but this would certainly complicate the development of science (why would someone infer the existence of an invisible mass to explain tides, for example ?). – StephenG - Help Ukraine Oct 14 '18 at 06:32