# Does GR put a theoretical lower limit on the radius of a black hole event horizon?

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

• 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 – CuriousOne Jun 5 '15 at 18:20
• 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. – CuriousOne Jun 5 '15 at 18:27
• @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. – Kyle Kanos Jun 5 '15 at 18:50
• @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. – CuriousOne Jun 5 '15 at 19:21
• 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. – CuriousOne Jun 5 '15 at 19:59

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.