Size of Black Hole: Swallow 1.5m x 3.585m x 20cm?

[Gramsci]

How big must a black hole be to swallow an object of 1,5m x 3,585m x 20 cm and how far away must it be to not swallow you and everything around you?

It's for a movie a friend is doing, and I really hope that you could answer the question or otherwise give me the formula and you would make my day.

/Magnus

 

[Hurkyl]

How big must a black hole be to swallow an object of 1,5m x 3,585m x 20 cm

Black holes don't get full. The only possible worry here is making sure the black hole exists long enough to devour the object. (Tiny black holes are expected to 'evaporate' quickly)

and how far away must it be to not swallow you and everything around you?

As long as you, and everything around you, avoid crossing the event horizon, you're fine.

 

[DaveC426913]

The thing to remember about black holes is that they are no different than any other massive object in the universe when it comes to gravitational attraction. Nothing gets "sucked in" to a black hole that wouldn't have gotten sucked into a garden-variety star of the same mass sitting in the BH's place.

If the sun suddenly up and collapsed into a black hole this very moment, then provided
1] we maintained the same distance from it as we are now, and
2] that the Sun didn't magically increase its mass,
the Earth would happily continue orbiting it as if nothing had happened.

Really.

A black hole of 1 solar mass, sitting where the sun sits, would have NO CHANGE on the Earth gravitationally.

This is an important concept to grasp.



That being said, the one tricky thing about a black hole is that you could get closer to its centre than a comparably massive object.

Our sun is 800,000 miles in diameter. 400,000 miles is as close as you're going to get, and as high a force of gravity as you're going to get.

But a black hole of the same mass as the sun might be only a few miles across. This means you could get - not 400,000 miles away - but a mere 1 mile away. THIS is where the huge gravitational forces come from.

 

[Nickelodeon]

and how far away must it be to not swallow you and everything around you?
/Magnus

From a purely speculative point of view, you could possibly get quite close to the fast spinning variety of black hole, provided you approached it from the right direction. The event horizon will not be uniformly globally distributed but be disc shaped. Approaching from a direction along the axis of spin and who knows you might even get pushed away.

 

[tarekkkkk]

black hole have asmall radius and inifinite mass and infinitegravity so what are you talking about is beyound your imagination...

 

[yuiop]

How big must a black hole be to swallow an object of 1,5m x 3,585m x 20 cm and how far away must it be to not swallow you and everything around you?

It's for a movie a friend is doing, and I really hope that you could answer the question or otherwise give me the formula and you would make my day.

/Magnus

Assuming the smallest possible black hole is a Planck mass (about the mass of ten human ovums ..did you know at one point in your life you weighed less than a Planck mass? :O) with a radius of two Planck lengths. In other words it would initially behave like a small grain of sand and move towards the nearest massive object. In our atmosphere it would simply fall towards the centre of the Earth, gathering mass and potentially "swallowing" the whole Earth.

Hawking's theory that such a small black hole would evaporate is not proven. Hawking showed that the surface area of a black hole is proportional to its entropy. The rules of the universe are that entropy either stays the same or increases in a closed system. As a black hole increases in mass so does the surface area of its event horizon and therefore its entropy increases. The evaporation of a black hole represents a loss of entropy which is against the laws of thermodynamics.

A rough description of Hawking's radiation works like this. Virtual particles spontaneously appear in the vacuum. Normally they mutually anhilate in a very short period of time. In the strongly curved spacetime near a black hole the anti particle of a virtual pair might fall into the black hole while the normal particle escapes. The antiparticle anhilates a normal particle inside the black hole. If the virtual pair were an electron and a anti-electron (positron) then the net effect according to Hawking is that the black hole has lost the mass of one electron and an one electron escapes.

The flaw in this argument is that when a positron and an electron inside the black hole anhilate they release two high energy photons. These two photons produced in the anhilation are still inside the black hole as they can not escape. The energy of the two photons still contribute to the mass of the black hole so the black hole has not lost any mass. In fact the the black hole has gained mass while the space outside the black hole has gained an electron. Another violation of the rules of the universe (if we assume energy conservation is a rule of the universe, but admitedly that is not clear in GR)

If there is no good reason why it is the normal particle that is "repelled" by the black hole while the anti-particle is attracted to the black hole, then it is equally statistically likely that the reverse occurs. In that case the black hole gains an electron and the universe gains a positron. Note that in both cases the the black hole gains mass. If the positron that escapes in the latter case meets up with an electron that escaped in the former case, then they anhilate releasing two photons. The net effect of the former case and the latter case is that the space outside the black hole has gained two normal photons and the black hole has gained two normal photons and a normal electron from the vacuum energy. If the energy of the two escaped photons is somehow returned to the vacuum then the overall loss of energy from the vacuum is two photons worth. The space outside the black hole has gained nothing and black hole has gained an electron and two photons. So overall the vacuum has lost two photons worth of energy and the black hole has gained two photons worth of erergy and the universe as a whole has gained an electron trapped in the black hole. Hmmm.. any accountants out there want to audit that?

Until we are certain that small black holes evaporate rapidly, it would not be prudent to create black holes in colliders on Earth. :P