AbstractThere are many talks about the Black Holes appeared recently after announcement by LIGO Scientific Collaboration about "Detection of Gravitational Waves from Black Holes". I tried to make simple calculation to see if it is possible to create very tiny Black Hole on the table :).
Practical applicationIs there any practical reason why we would like to have the Black Hole on the table? First of all it is fun to have something unusual :), but really it can be used for garbage disposal. Can you imagine, you throw some trash to the tiny object and it disappears immediately without using any space and without any traces. Very useful :)
Size and mass calculation
I would not be very greedy and ambitious and calculate just tiny Black Hole with diameter 0.1 mm. I will use Schwarzschild radius or gravitational radius formula for this calculations. This radius means if we compress anything to this radius, it will become Black Hole and nothing can escape from it, if it fall below this radius, even light. It is well known from this link, that for the Earth this radius equals 9.0 mm.
and calculate mass for 0.1 mm Black Hole. It will be 3.37*1022 kg (33700000000000000000000 kg). It just 0.5% (1/200) of the Earth mass or 40% of the Moon mass. It is not very small mass and can lead to some small deviation in the Earth orbit and rotation. But let's make further calculations :)
How to get this amount of matter?Of course we cannot simply collect this amount of substance and squeeze it. But what we can do? We can use famous Einstein formula E=mc2. In other word if we will take a small metal sphere and will rotate it very quickly at some point it will become the Black Hole. What should be rotation speed and how much energy do we need? Simple calculation shows that rotation speed will be 6.5*1027 (6500000000000000000000000000) rotation per second and we need 3*1039 Joules (3000000000000000000000000000000000000000 Joules) of energy. 3*1039 J of energy standard power plant with power 1000Mwatt will produce in 9.6*1022 years (96000000000000000000000 years). Rotation speed is such high, that edge of our metal sphere will be moving faster than speed of light. It is not possible and if we use Special Theory of Relativity we will get the speed which just 1.4*10-53% less than speed of light and it corresponds to 9.55*1011 rotations per second (955000000000). Any way such high speed is not possible, because any material will be broken by centrifugal force.
What will be the impact of this tiny Black Hole?
Though it looks impossible to create this kind of the Black Hole, let's assume that we have it. We need to understand how dangerous it could be. If we will stay 1 meter from this Black Hole the gravitational force will be 225 000 000 000 times (2.25*1011) more than we have on the Earth surface. Definitely we cannot escape anyhow from it and we will be sucked inside it. Distance around 475 km gives as the same force as we have on the Earth surface. It is still to much to put in on the table. To be on the safe side I personally prefer not to come closer than 5000 km where this force will be 100 times less than on the Earth surface. Also we should not forget about Black Hole Evaporation. Our tiny 0.1mm Black Hole will be very stable and evaporates only in 1044 years (100000000000000000000000000000000000000000000 years).
What will happen if the Earth will collide with that Black Hole?
Basically this Black Hole will make a hole in the Earth with diameter 30 km (where gravity 1000 times higher than Earth) and will suck in everything inside this 30 km hole.
Safe Black Hole
If we want to create "safe" Black Hole, for example that in 10 cm it's gravity 100 times less than on the Earth surface, it should have diameter about 4.5*10-20 m (0.000000000000000000045 m or 100000 times less than proton) and mass 15000000 kg (15000 tons). If we want to make it from energy standard 1000 MWatt power plant will need just 40 million years. It will be dangerous only in 1 mm distance, where gravity will be 100 times more than on the Earth. If we make a line of these Black Holes we can get a very nice weapon Blackholesaber. It will make a nice 1 mm hole in everything. But it will be difficult to have a saber battle like in Star Wars. 2 Black hole sabers will suck in each other and make a new bigger Black Hole. Only problem with such a small Black Hole will be evaporation. Because it is very small, it will evaporate completely in 3 days. In order to prevent it, we will need to feed it :) And it will eat very very much, around 50 kg per second. Another trouble it can bring, if we will not feed it, it will evaporates faster and faster and finally it will be a big explosion. For example if we will have 0.8 gram black hole it will evaporate extremely fast (1.4*10-33 seconds or 0.0000000000000000000000000000000014 seconds), which will actually means explosion with 15 kilotons of TNT (like in Japan during WWII).
First of all, it is not possible to create even 0.1mm Black Hole with current technologies. It is a positive news :) But if somebody will make it, it will be not possible to keep it on the table. Most probably creator will be sucked in. Very small Black Holes around 1 kg can be used as weapon. 1kg Black Hole will be bursting immediately as 10 Megatons of TNT.