Friday, April 30, 2010

Dinner With a Black Hole

A number of people have asked: If Earth contained a tiny Black Hole, wouldn't we be sucked up? This shows a common misconception, even among PhD's. A Black Hole, even nearby, would not swallow you. We can illustrate this around the dinner table.

Suppose you are seated at the dinner table, about one meter from the table's centre. The hostess surprises you by placing a primordial Black Hole on the table. The Universe is thought to contain billions and billions of these tiny holes. They were formed from tiny quantum fluctuations grown large by the rapid expansion of the Universe. Typical mass of a primordial Black Hole is about 10^11 kg.

This Black Hole with the mass of Diamond Head, would have a Schwarzhild radius of:

2GM/c^2

The 10^11 kg hole has a diameter of just 10^(-16) meters, less than the size of a proton!

Sitting at the table, the gravitational acceleration you would feel is given by:

GM/r^2

Where G is Newton's gravitational constant, M is Mass of the Black Hole and r is your distance.

This is easy to calculate. G = 6.67 x 10^(-11), M is 10^11 kg and r = 1 meter. The acceleration you would feel is just 6.67 m/sec^2, barely 2/3 that of Earth's gravity! If you braced yourself against the table, you would not fall into the Black Hole.

Suppose that you were suicidal and reached for the Black Hole. As soon as you touched the event horizon, a portion of your finger would be converted into radiation according to E=mc^2. If your fingertip weighs 1 gram, the radiation released would be 9 x 10^13 Joules, equivalent to a small nuclear explosion! The rest of you would be blown sky high, easily exceeding the Black Hole's tiny escape velocity. Your charred remains would never bother the Black Hole again.

As for the table, a small amount would be swallowed by the Black Hole, releasing enough radiation to keep the everything else away. The immediate vicinity would become a swirling mass of charged particles. If enough charged mass orbited the Black Hole, iot would generate a magnetic field like that of Earth.

Sitting to dinner with a Black Hole, a person could not be swallowed even if he wanted to. The Black Hole would create radiation and possibly a magnetic field, just like Earth's centre. As we eat dinner tonight, we have reason to consider a Hole in the Earth.

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nige said...

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1:49 PM
nige said...

Thanks for the calculation, which really does show how weak gravity is, that you would need a huge mass on your dinner table to feel any acceleration towards it! It reminds me that Frederick Soddy, the discoverer of isotopes, pointed out the strength of electromagnetism by saying that 2 grams of protons placed at the opposite poles of the earth would repel with a force equivalent to that from 26 tons of mass in a gravitational field.

Do you have any ideas about how the tremendous pressures of molten rock deep inside the earth could be stopped from making material enter a black hole there, causing it to grow and rapidly swallow up the whole planet? Even with a weak gravitational field around a black hole, matter will still be pushed at it. It just doesn't look a very stable situation to me. If Hawking radiation emission from the black hole is supposed to be keeping other matter at a safe distance, then some matter would need to be falling in to compensate for the energy loss and keep the situation stable for 4,540 million years. This problem reminds me of the Dyson sphere. Freeman Dyson had the idea in (I think) his book Disturbing the Universe that in the very distant future when the stars have all run low on fuel, people will use all the mattter available to build shells around stars, to conserve the heat energy. The shell is then heated on the inside by the star.

I think your idea of trapped black holes is mainly of interest in this Dyson reactor sense. The energy of the emitted "Hawking" gamma rays depends on the radiating temperature of the black hole, but if it is not too high then those gamma rays can be stopped by moderate thicknesses of matter (the Compton scattering effect), converting the gamma ray energy by successive scatters into the energy of Compton electrons, which rapidly gets converted into heat by ordinary charged particle collisions with matter. So you could use a trapped radiating black hole as an energy source. Toss any matter you like into it, and you get heat output via gamma rays and the Compton effect.

It would be an alternative to fission and fusion (which can only turn a very small mass defect in light or heavy elements into energy). It would also be clean because you would get no induced radioactivity from neutrons which you do in fission and fusion. Gamma rays of low to moderate energy don't induce radioactivity. Just throw waste into the black hole, and get energy as your output. A perfect garbage disposal unit and a perfectly efficient energy source.

1:50 PM
Zephir said...

/*..if enough charged mass orbited the Black Hole, iot would generate a magnetic field like that of Earth..*/

This magnetic field would be a much stronger and it would literally drag surrounding matter into resulting vortex in much faster speed, then the NH gravity.

3:50 PM
Anonymous said...

Wouldn't such a tiny black hole evaporate very quickly via Hawking radiation?

7:19 AM
Ulla said...

It doesn't either explain the expanding Earth. The Earth grows not steadily but in pulses. Can a black hole have avariable activity?

Actually I am not at all worried the black hole would swallow the Earth, more the opposite, it would evaporate and leave us with the fate of Mars.

I think your digestion is not very effective :)

9:03 AM
Qubit said...

It just can't be done. Its a lie.

11:17 AM
Ulla said...

Here is something for you.
http://www.newscientist.com/article/mg20627564.900-dark-matter-may-give-neutron-stars-black-hearts.html
Dark matter may give neutron stars black hearts

DARK matter may be prompting black holes to appear spontaneously in the hearts of distant exotic stars.

each particle of the stuff is also an antiparticle, meaning that they should annihilate each other when they meet. But Fairbairn and de Lavallaz considered a dark matter particle of a different type, which is not also its antiparticle.

Because they would not annihilate each other, the dark matter particles would end up forming a smaller, dense star at the heart of the neutron star.

the existence of dark matter particles that do not self-annihilate cannot be ruled out.

This would explain the planet core, the orbiting planets that not are destroyed although they orbit too near an star.

What is the Higgs field exactly? Maybe the ether still has to be reborn? What are those theorethical H-spinors?

7:38 AM
Ulla said...

http://physicsworld.com/cws/article/news/42270
http://arxiv.org/abs/1004.0386

However, a team of researchers, led by Chris Belczynski report that these projects have taken the wrong option, saying that double black hole systems may be far more common than previously thought. The reason is related to stars' metallicity, which is the fraction of elements that are heavier than helium. The lower the metallicity the less mass is lost at the end of the star's life and therefore the black holes that form are more likely to survive to become a black hole binary.

The finding is particularly significant given the sensitivity of black hole binary formation to changes in metallicity. "If you reduce metallicity by a factor of ten then you increase the number of black hole binaries by a hundred or a few hundred times,"

8:53 AM
Ulla said...

http://www.sciencemag.org/cgi/content/abstract/science.1186212

we propose that the growth of the solid core implies an eastward drift of the material, driven by crystallization in the Western Hemisphere and melting in the Eastern Hemisphere.

9:10 AM
Ulla said...

If magnetic monopoles exist, they probably formed just after the Big Bang that is thought to have started off our universe. Back then, when all of space was much hotter and denser than it is today, there might have been enough energy to form monopoles.

From http://www.livescience.com/strangenews/lhc-magnetic-monopole-100331.html

What if that magnetic monopole is pronounced 'primordial black hole'? There are a difference in size but how is it in theory?

Or could it be pronounced 'wormhole'?

10:09 AM
Anonymous said...
5:46 AM
LCc 03 said...
3:34 PM