Micro-Black Holes

[GeeKay]

Hi

 

I understand that micro-black holes probably don't exist in nature - at least it would appear to be the case, according to current received wisdom on the subject. Be that as it may, I would be interested to learn about the properties of such objects. As an example: if one posits a MBH with (say) the mass of Phobos (vital statistics: 22.2 Km diameter; mass: 1.08 x 10*16 Kg) how small would the event horizon be, for example? Also, in view of the gravitational tides, how near would a person be able to approach such a collapsed object without risk to life and limb? An inch? A metre? Half a furlong? I must admit that my maths isn't all that good at present - although I'm doing my level best to rectify this situation. Still, I would appreciate a largely non-mathematical, 'lay reader' style response, if at all possible. Many thanks for hearing me out.

 

GeeKay

[pwagen]

Haha - "furlong". That's brilliant!

 

Anyway, the Schwarzchild radius of a black hole acts as its event horizon. You get the Schwarzchild radius of an object from [latex]r_s=2Gm/c^2[/latex], where G is the gravitational constant, m is its mass and c is, of course, the speed of light.

 

For Earth, the Schwarzchild radius is about 9 mm, so I'm guessing Phobos' would be smaller. So, inserting what we know about this little moon into the equation, we get something like [latex]1.6*10^-11[/latex] meters, or 0.016 nanometers.

 

As for how close you'd be able to get to it, that's for someone else to answer. The Wikipedia page seems to suggest it will simply pass straight through without interacting with other matter.

 

http://en.wikipedia.org/wiki/Micro_black_hole

http://en.wikipedia.org/wiki/Event_horizon#Event_horizon_of_a_black_hole

[SamBridge]

Micro black holes can theoretically exist, but due to the uncertainty in their energy modeled by Hawking Radiation the micro black holes would only exist for an instant before they would evaporate.

[GeeKay]

0.016 nanometres? That is a small radius, indeed! Yes, about the effects of Hawking radiation, this quantum effect I do understand. I just wonder at what level of mass is required for it to begin to have a drastic effect upon the MBH concerned. Also, I wonder if I had been somewhat vague in using the word 'micro' to describe what otherwise could be referred to as 'mini' or 'primeordial' black holes. But then, hey, what's in a name? Still, I mention this because, while accepting that such objects must be accounted truly minuscule in the grand scheme of things, nonetheless there would appear to be an appreciable difference - leastways in terms of observable effects - concerning MBHs ranging in mass between those of small mountains to seriously large asteriods. Another way of addressing the problem would be to put it like this: at what minimal mass would such a hyphothetical MBH need to be for it to exhibit the sort of effects I posited in my original post? In other words (once again dragging the observer into the experiment) at what distance could a person safely remain before feeling the gravitational effects from such an object? By the by, I have a fourteen-year old niece who is mad on astronomy and who likewise is also very keen to know the answer to this seemingly unfathomable question. Many thanks again.

 

GeeKay

[ACG52]

Outside of it's event horizon, the gravity of a micro or mini black hole is no more that the gravity of the mass comprising it. Given the minuscule gravity of the original mass, and the minuscule size of the eh, it could probably pass right through you and you'd never feel any effect.

[Moontanman]

If Hawking is correct a MBH of the mass of phobos would be like a traveling nuclear explosion, radiating away enormous amounts of energy, the smaller the black hole the faster they evaporate so the size is important but in an inverse way...

https://en.wikipedia.org/wiki/Hawking_radiation

[SamBridge]

0.016 nanometres? That is a small radius, indeed! Yes, about the effects of Hawking radiation, this quantum effect I do understand. I just wonder at what level of mass is required for it to begin to have a drastic effect upon the MBH concerned. Also, I wonder if I had been somewhat vague in using the word 'micro' to describe what otherwise could be referred to as 'mini' or 'primeordial' black holes. But then, hey, what's in a name? Still, I mention this because, while accepting that such objects must be accounted truly minuscule in the grand scheme of things, nonetheless there would appear to be an appreciable difference - leastways in terms of observable effects - concerning MBHs ranging in mass between those of small mountains to seriously large asteriods. Another way of addressing the problem would be to put it like this: at what minimal mass would such a hyphothetical MBH need to be for it to exhibit the sort of effects I posited in my original post? In other words (once again dragging the observer into the experiment) at what distance could a person safely remain before feeling the gravitational effects from such an object? By the by, I have a fourteen-year old niece who is mad on astronomy and who likewise is also very keen to know the answer to this seemingly unfathomable question. Many thanks again.

 

GeeKay

Any terrestrial object that created a black hole would be no problem, even if the entire Earth became a black hole it's radius would only be what I calculate to be around .008 meters.

It's also important to point out that you never "feel" gravity, so for any micro black hole, you'd essentially have to come into direct contact with it to notice anything. The only time you would actually "feel" anything is with very large black holes at least a solar mass where your body would get stretched out and ripped apart which I don't know exactly when that would happen, but for a 1 solar mass black hole I'd guess the orbit of Mercury is safe enough to not be ripped to shreds.

Edited June 12, 2013 by SamBridge

[GeeKay]

I don't know if this is worth bringing to the party, but with regards to Hawking radiation and possible local gravitational effects concerning MBHs, this may be of interest:

 

http://casa.colorado.edu/~ajsh/hawk.html

[MigL]

You actually do 'feel' gravity, Sam, as a result of tidal forces.

These forces are actually more pronounced for smaller BHs than for larger ones.

You could be at twice the event horizon's radius of a stellar sized BH and not feel any tidal forces, while you would feel tidal forces at ten times the radius of the event horizon for an earth sized BH.

 

The energy ( Hawking ) density radiated by black holes increases as they get smaller because volume decreases as the cube of the radius of the event horizon but the surface area decreases less slowly, as the square of the radius. At a certain point ( size ) all the remaining mass is converted to radiation and emitted as a gamma ray burst. This would be a large amount of mass ( still ) undergoing 100% conversion to energy; I don't think you'd want to be close by when that happens.

Edited June 16, 2013 by MigL

[GeeKay]

Yes, I understand. I know this must be obvious to many, but it isn't to me. The 'sensation' of gravity that one feels would appear to be entirely due to its differential tidal pull. And since spheres offer the minimum surface area for mass (MigL's point about the variability between surface area and volume over size notwithstanding) this means that gravity, or 'curved space' must always have a tidal pull associated with it. This gives gravity its sense of 'direction' - at least in the universe we inhabit. Or am I off-target here?

 

On a different point, I've had it pointed out to me that a 11 billion tonne MBH would exert a one third gravitational pull (G) at a distance of 15 metres. Now I don't have the maths, but given that a MBH with the mass of Phobos is around 10.8 trillion tonnes, I would imagine an observer would feel a heck of a lot more than 0.3 G at the same distance. Only a half-educated guess, mind.

[Airbrush]

"...at what distance could a person safely remain before feeling the gravitational effects from such an object?"

 

Let's use the Earth for an example. If Earth was crushed into a black hole, it would be about the size of a marble. You could orbit this black hole safely, but you would need to be over 4,000 miles from it. With an asteroid-mass, primordial black hole, you would also need to keep a good distance away to orbit it safely.

 

We don't know if any primordial, mini-sized black holes still exist, but I think they could be any size, depending upon how much mass they have, which could vary a great deal.