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Within GR theory, without going to the extreme r/0 as a radius, (but approaching that as an asymptotic case), is there any theoretical limit as to how small the event horizon of a rotating and/or charged black hole can be?

I appreciate that the Hawking radiation hypothesis postulates that micro black holes, especially primordial ones, should be hard to find, due to evaporation although, as far as I know, this is still a speculative idea, with unfortunately no definitive data to confirm or falsify it.

I am also aware of the possible basis of Planck lenght effects, but again, as far as I know, these are speculative ideas, without observational proof.

To sum up, I want to ask this question regarding GR within the observational effects we have already confirmed.

EDIT apart from CuriousOne's comment, which is true of course, I need 1 assumption for this particular question! END EDIT

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    $\begingroup$ There is no data for GR event horizons, either, so it's pretty much all speculation. Can I offer you a turtle on the way down until we have a way of imaging the first dozen black holes, or so? Alternatively, you could petition your congressman for funding for something like this: bhi.gsfc.nasa.gov $\endgroup$
    – CuriousOne
    Commented Jun 5, 2015 at 18:20
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    $\begingroup$ No offense taken, personally I am happy with long distance recon with telescopes of whatever sort gets the job done and I hope that the first black hole event horizon data will be produced within my lifetime (I might be too senile to understand it, though). Of course, if all we were to learn is that GR holds tight, then we wouldn't have learned anything new in like 120 years, or so... I hope that's not how it will turn out. As for Planck scale effects, there is a bunch of folks who advertise the idea that quantum gravity should lead to x-ray birefringence... so that might be a discovery path. $\endgroup$
    – CuriousOne
    Commented Jun 5, 2015 at 18:27
  • $\begingroup$ @CuriousOne: With respect to "BH event horizon data in your lifetime," you may be interested in the Event Horizon telescope (and their publications) which was designed to observe the scale of Sgr A*'s event horizon. $\endgroup$
    – Kyle Kanos
    Commented Jun 5, 2015 at 18:50
  • $\begingroup$ @KyleKanos: Thanks for the link. I know about them, but I thought they were still a little short (maybe by a factor of two or three) although they are imaging at the scale of the object now. The reconstructed images in arXiv:1404.7095 could make one believe that what we are seeing there is the black hole... but one has to be careful, at least I believe they are using models in the reconstruction (they say for total flux only?), so it's not totally unbiased data in my opinion. I admit that I don't quite understand how they are reconstructing, so I might be wrong. $\endgroup$
    – CuriousOne
    Commented Jun 5, 2015 at 19:21
  • $\begingroup$ Yeah... it's bootstraps and giant foam hands waving... that kind of thing. I was thinking about this kind of prediction for the optical (and it seems to extend into the x-ray/gamma region): arXiv:gr-qc/0102093 or mnras.oxfordjournals.org/content/376/4/1857.full... don't worry, I am not taking these too seriously, either. $\endgroup$
    – CuriousOne
    Commented Jun 5, 2015 at 19:59

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General Relativity is a purely geometrical theory of gravitation. Quantum effects have no place within GR, and more generally there is no scale to GR itself.

For example, if you look at the Schwarzschild solution, you can set the mass $M$ to be whatever you want. But if you change $M$, you can also scale the time coordinate $t$ and the radial coordinate $r$ so that this has no effect. To be specific, just define new quantities \begin{align} M' &= 2M, \\ r' &= 2r, \\ t' &= 2t. \end{align} This also gives you a Schwarzschild solution. Plug in any (nonzero) number instead of $2$, and you've got another solution. This is why we can't derive the length of a second from GR (we arbitrarily choose it related to a frequency found in quantum effects). Instead, you can only derive scale-invariant ratios.

Of course, GR is only an approximation to what scientists believe is the correct theory of the universe. And there are regions of parameter space where that approximation is believed to be wrong. One of these is at the very small scales where quantum effects are strong, which is why the Planck length might come into it.

So within GR itself, there are no limits. But GR isn't the end of the story, and we don't know the end of the story yet.

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  • $\begingroup$ thank you very much for that, it was mainly for confirmation but also to learn a bit more (as a total GR newbie and born again complete pragmatist, ever since I restarted physics studies), I wanted to build another question based on this one. much appreciated $\endgroup$
    – user81619
    Commented Jun 5, 2015 at 18:55

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