Using a black hole as a weapon

[Dr Chaos]

Would it be possible to use a black hole as a weapon?

What I was thinking is that you could use a very powerful gun and some very dense material to make a black hole projectile. All you would need is a bullet in the shape of an elongated sphere with some extremely dense material inside. What would happen, is that the bullet would be fired at such a speed that it lorentz-contracts into its Schwarzschild radius and becomes a very micro black hole. Is this idea plausible? I am quite sure that you cannot move a black hole but can it maintain original momentum? What it is I am struggling with is trying to find the perfect ratio of speed (and lorentz factor) to mass (and lifetime).

Useful formula:

$$\gamma \equiv \frac{1}{\sqrt{1 - v^2/c^2}}$$

Lifetime = 10^-28 M³

Where M is mass in grams.

 

[tiny-tim]

Hi Dr Chaos!

What would happen, is that the bullet would be fired at such a speed that it lorentz-contracts into its Schwarzschild radius and becomes a very micro black hole.

The bullet's width stays the same.

 

[DocMuffinZ]

Not a good weapon, even theoretically. Try not to hurt your back loading a bullet that massive XD

 

[Jonathan Scott]

Would it be possible to use a black hole as a weapon?

What I was thinking is that you could use a very powerful gun and some very dense material to make a black hole projectile. All you would need is a bullet in the shape of an elongated sphere with some extremely dense material inside. What would happen, is that the bullet would be fired at such a speed that it lorentz-contracts into its Schwarzschild radius and becomes a very micro black hole. Is this idea plausible? ...

No, it isn't plausible. It's the Schwarzschild radius in the bullet's own rest frame which matters.

The total energy in a projectile moving near c is essentially equal to whatever kinetic energy you put into it (to the extent that the rest mass can be ignored). Even if you had the means to make the projectile into a micro black hole that would make it a LESS effective weapon, as it would minimize its cross-section to the extent that it would do much less harm than the original bullet, passing right through most materials.

 

[Count Iblis]

I agree with Jonathan, you really have to somehow compress the object to within its own Schwarzschild radius. Now, if you make a micro black hole, then that black hole will emit lethal amounts of Hawking radiation, so it could be a used as a weapon...

The momentum will actually not stay zero because of the stochastic nature of the emitted radiation. So, while the photons are emitted with equal probability in all directions, you will have statistical fluctuations. The black hole will thus move like a random walker.

 

[PaulS1950]

From an action / reaction point of view this would never work.
If your "gun" weighs as much as the black hole you are going to shoot then the black hole will move at 1/2 the expected velocity and the gun will move in the reverse direction at the same speed. If you are talking about just 3000 fps then both the gun and bullet would move in opposite directions at 1500 fps.
How would you make a gun that has the weight of a black hole? what would you use to propel a bullet that absorbs all matter and energy that gets close enough to act upon it?

Not even conceptually possible.

 

[Dr Chaos]

The bullet's width stays the same.

I know that; that is why I said the bullet would be in the shape of an elongated sphere - so it lorentz contracts into a spherical shape.

Now, for the mass of the bullet and its practicality, here is what I propose:
The bullet is fired at an extremely high speed. Thus, the mass increases by a substantial amount while the bullet is moving and the Schwarzschild radius is then increased. This is good because it doesn't really need to have a ridiculously large mass to begin with.

I just need to find some plausible values to satisfy all of this.

 

[Jonathan Scott]

I know that; that is why I said the bullet would be in the shape of an elongated sphere - so it lorentz contracts into a spherical shape.

Now, for the mass of the bullet and its practicality, here is what I propose:
The bullet is fired at an extremely high speed. Thus, the mass increases by a substantial amount while the bullet is moving and the Schwarzschild radius is then increased. This is good because it doesn't really need to have a ridiculously large mass to begin with.

I just need to find some plausible values to satisfy all of this.

Making something move very fast has no effect on its self-gravitation in its own rest frame. Lorentz contraction is only from other viewpoints, not its own viewpoint.

 

[Dr Chaos]

Making something move very fast has no effect on its self-gravitation in its own rest frame. Lorentz contraction is only from other viewpoints, not its own viewpoint.

So you can't lorentz-contract something to make it more dense?

 

[IcedEcliptic]

If you had such energy at your disposal, kinetic weaponry is best, for explosion, and depending on the material, radiation.

 

[IcedEcliptic]

So you can't lorentz-contract something to make it more dense?

Perhaps if you spun it while compressing it from all angles? It would take unthinkable energy. Perhaps you create MBHs with an accelerator, and use some kind of Alcubierre drive mechanism, to move the hole and fire that?

 

[DaveC426913]

Perhaps if you spun it while compressing it from all angles? It would take unthinkable energy. Perhaps you create MBHs with an accelerator, and use some kind of Alcubierre drive mechanism, to move the hole and fire that?

Yes, but as with all solutions that are going to come out of this, once you're harvesting the vast enegies required, why bother with the BH? Just turn your gun on your target and open er up. Whatever's in there to tame a BH is surely enough to put a hole in someone's gunwale.

 

[IcedEcliptic]

Yes, but as with all solutions that are going to come out of this, once you're harvesting the vast enegies required, why bother with the BH? Just turn your gun on your target and open er up. Whatever's in there to tame a BH is surely enough to put a hole in someone's gunwale.

I agree, this is why I first said: "If you had such energy at your disposal, kinetic weaponry is best, for explosion, and depending on the material, radiation."

 

[DaveC426913]

I agree, this is why I first said: "If you had such energy at your disposal, kinetic weaponry is best, for explosion, and depending on the material, radiation."

Yeah. That was aimed at the OP, not you.

 

[Jonathan Scott]

So you can't lorentz-contract something to make it more dense?

Correct.

 

[LURCH]

Try this simple thought experiment:

Start with a neutron star that just barely lacks enough mass to become a black hole. Accelerate that object to near light speed, and its apparent mass is multiplied thousands of times. The neutron star now becomes a black hole with a an event horizon at a certain radius, R.

Orbiting around that neutron star there is a satellite with a highly elliptical orbit. This elliptical orbit goes from ½R out to 2R. You now have a satellite repeatedly falling into and then exiting from the event horizon of a black hole. This is a situation that cannot exist in the real world, and it is the situation that must necessarily exist if one could turn an object into a black hole by accelerating it.

Therefore, one cannot turn an object into a black hole by accelerating it.

 

[Dr Chaos]

Try this simple thought experiment:

Start with a neutron star that just barely lacks enough mass to become a black hole. Accelerate that object to near light speed, and its apparent mass is multiplied thousands of times. The neutron star now becomes a black hole with a an event horizon at a certain radius, R.

Orbiting around that neutron star there is a satellite with a highly elliptical orbit. This elliptical orbit goes from ½R out to 2R. You now have a satellite repeatedly falling into and then exiting from the event horizon of a black hole. This is a situation that cannot exist in the real world, and it is the situation that must necessarily exist if one could turn an object into a black hole by accelerating it.

Therefore, one cannot turn an object into a black hole by accelerating it.

Is it not the behaviour of the satellite that is impossible? Why does it exit the event horizon? Also it would be extremely difficult to maintain an orbit like that at such speeds anyway. I don't understand how you can make something smaller and increase its mass without altering its density.

 

[IcedEcliptic]

Is it not the behaviour of the satellite that is impossible? Why does it exit the event horizon? Also it would be extremely difficult to maintain an orbit like that at such speeds anyway. I don't understand how you can make something smaller and increase its mass without altering its density.

Make it smaller yes, but that requires adding energy to compress. Contraction due to acceleration is a matter of the frame of reference, I think. You need more than a relativistic effect: added mass/compression.

 

[LURCH]

Is it not the behaviour of the satellite that is impossible? Why does it exit the event horizon? Also it would be extremely difficult to maintain an orbit like that at such speeds anyway...

It is indeed the behavior of the sattelite that is impossible. But keep in mind that all motion is relative, so if you are traveling past the nuetron star at near lightspeed, that is the same as saying the star is traveling past you. So it is no m,ore difficult to maintain the orbit "at such speeds" than it would be at rest, because the star is in fact at rest in its own refference frame.

So again, the sattelites behavior is impossible, and would inevitably arise from the original premise. Therefore, the premise is incorrect.

 

[Dr Chaos]

So is there a relativistic Schwarzschild radius for a moving object? If our sun is accelerated to 0.9 c, what is its Schwarzschild radius?

 

[Jonathan Scott]

So is there a relativistic Schwarzschild radius for a moving object? If our sun is accelerated to 0.9 c, what is its Schwarzschild radius?

It's no different from the radius of any other spherical entity. In the forward and back direction it is Lorentz contracted, but in the sideways direction it is not affected.

 

[IcedEcliptic]

No addition of mass, or no compression = no black hole. contraction of a star can compress matter as needed, and it is believed that neutron stars can accrete matter and collapse further. If you had unthinkably powerful lasers you could use a hohlraum a la the NIF to compress material, or perhaps the collision of energetic particles in a collider, but no relativistic effect alone can achieve what you want. This compression would have to be valid in all frames, including the frame of the sun.

 

[Dr Chaos]

No addition of mass, or no compression = no black hole.

But there is an addition of mass when an object is accelerated.

It's no different from the radius of any other spherical entity. In the forward and back direction it is Lorentz contracted, but in the sideways direction it is not affected.

I realize that the sideways direction is not affected; the bullet would be elliptical in shape and its sideways radius would be equal to its Schwarzschild radius and its length would be equal to the Schwarzschild radius multiplied by the Lorentz factor or $$\frac{2GM}{c^2}$$$$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

*I seem to be having issues with LaTeX - use this site to convert the source code if you really want to see the formula.

 

[Jonathan Scott]

But there is an addition of mass when an object is accelerated.

A fast moving object has additional energy due to its motion. However, from a frame where that object is at rest (such as its own frame) there is no additional energy.

 

[tiny-tim]

An object which is a black hole in one inertial frame will be a black hole in any inertial frame.

Since this bullet obviously isn't a black hole in its own frame, it isn't one in any frame.

 

[Dr Chaos]

Ok, try this:

The bullet has a mass of 2.019892435*10²⁵ kg
The bullet's sideways radius is 0.03 m
The bullet's length is [strike]0.0375 m[/strike] 0.075 m

The bullet is then accelerated to 0.6c or 179875474.8 ms^-1, and it is Lorentz-contracted into a spherical shape with the radius 0.03 m, the same as its Schwarzschild radius. It becomes a black hole in the reference frame of the observer but perhaps not in its own reference frame? Is this some sort of paradox?

 

[tiny-tim]

The bullet is then accelerated to 0.6c or 179875474.8 ms^-1, and it is Lorentz-contracted into a spherical shape with the radius 0.03 m, the same as its Schwarzschild radius. It becomes a black hole in the reference frame of the observer …

No it doesn't!

Imagine that the bullet is glowing, and consider the point F at the "front" of the bullet … can the glowing light escape?

A photon at F feels the gravity of each point in the bullet, dependent on r, where r is the distance that that point was from F "when the gravity left it".

For example, for a point on the centre line of the bullet, distance x from F (in the frame in which the bullet's speed is v) …

then r is measured from its position at time minus t, where vt + x = ct = r, ie t = x/(c-v) and r = x(1 + v/(c-v)) = x/(1 - v/c) …

x in the "stationary" bullet was y, where Lorentz contraction means that x = y√(1 - v²/c²),

so the overall "contraction" is √(1 - v²/c²)/(1 - v/c) = √(1 + v/c) / √(1 - v/c) … which isn't a contraction!

(For example, if v = 0.6, that's r = x/0.4 = 5x/2 = 0.8*5y/2 = 2y)

ok, now you work out what it is for the point B at the back of the bullet! ​

 

[IcedEcliptic]

No it doesn't!

Imagine that the bullet is glowing, and consider the point F at the "front" of the bullet … can the glowing light escape?

A photon at F feels the gravity of each point in the bullet, dependent on r, where r is the distance that that point was from F "when the gravity left it".

For example, for a point on the centre line of the bullet, distance x from F (in the frame in which the bullet's speed is v) …

then r is measured from its position at time minus t, where vt + x = ct = r, ie t = x/(c-v) and r = x(1 + v/(c-v)) = x/(1 - v/c) …

x in the "stationary" bullet was y, where Lorentz contraction means that x = y√(1 - v²/c²),

so the overall "contraction" is √(1 - v²/c²)/(1 - v/c) = √(1 + v/c) / √(1 - v/c) … which isn't a contraction!

(For example, if v = 0.6, that's r = x/0.4 = 5x/2 = 0.8*5y/2 = 2y)

ok, now you work out what it is for the point B at the back of the bullet! ​

LOL, you're mean. ;)

 

[LURCH]

It becomes a black hole in the reference frame of the observer but perhaps not in its own reference frame? Is this some sort of paradox?

Yes, this is exactly the paradox referenced earlier. In the bullet's reference frame, it can impact objects and those objects can bounce off of the surface of the bullet. To the outside observer, these objects cannot bounce off because they are tuoching the event horizon of a black hole. So the objects both do and do not bounce off of the bullet. Paradox.

 

[Dr Chaos]

No it doesn't!

Imagine that the bullet is glowing, and consider the point F at the "front" of the bullet … can the glowing light escape?

A photon at F feels the gravity of each point in the bullet, dependent on r, where r is the distance that that point was from F "when the gravity left it".

For example, for a point on the centre line of the bullet, distance x from F (in the frame in which the bullet's speed is v) …

then r is measured from its position at time minus t, where vt + x = ct = r, ie t = x/(c-v) and r = x(1 + v/(c-v)) = x/(1 - v/c) …

x in the "stationary" bullet was y, where Lorentz contraction means that x = y√(1 - v²/c²),

so the overall "contraction" is √(1 - v²/c²)/(1 - v/c) = √(1 + v/c) / √(1 - v/c) … which isn't a contraction!

(For example, if v = 0.6, that's r = x/0.4 = 5x/2 = 0.8*5y/2 = 2y)

ok, now you work out what it is for the point B at the back of the bullet! ​

Could I please have a diagram for this? I can't make sense of the maths.

Yes, this is exactly the paradox referenced earlier. In the bullet's reference frame, it can impact objects and those objects can bounce off of the surface of the bullet. To the outside observer, these objects cannot bounce off because they are tuoching the event horizon of a black hole. So the objects both do and do not bounce off of the bullet. Paradox.

And what is the solution? That a bullet cannot become a black hole by acceleration? I agree that it does not become a black hole in its own frame of reference. What I cannot understand is that based on measurements taken by the observer in his or her reference frame, (like mass and radius), he or she would conclude that it actually is a black hole. Maybe that is what is paradoxical.

 

[Dmitry67]

The very calculation for the Schwarzschild radius are done in stars rest frame

If the same star is flying by at very high speed, it is in fact Lorentz-contracted, but, the same math is no longer applicable for the Schwarzschild radius! The solution is now dynamic (as star is flying) and it becomes very different because in General Relativity gravity is not created by mass but by stress energy tensor, which insludes rest mass as just one of its components.

Example: photon gas. Rest mass: zero. But it creates gravity because it has pressure.

 

[Dmitry67]

Oversimplification. Flying object has less gravity.

Imagine 2 objects flying in parralel at very high speed. In their own rest frame they attract to each other. However, when they fly by there is a time dilation, so they attract slower, so external observer concludes that the force between them is weaker.

Again, it is an oversimplification.

 

[Dr Chaos]

Okay, I understand now. Thanks to everybody who posted.

However, I do have another question. If the bullet is a black hole in its resting frame of reference (i.e. so it is actually a black hole), and if I was to accelerate it, what would its behaviour be like in Earth's atmosphere? Would it slow down quickly or could it maintain a constant velocity?

 

[Dmitry67]

Black hole in a gas?
In would 'eat' all gas around it, it mass would increase, and it would slow down (because momentum is conserved). However, very soon it will create powerful jets from the poles. These jets will be very intensive. They will carry away the momentum affecting the trajectory of the black hole.

 

[Ich]

Would it slow down quickly or could it maintain a constant velocity?

It would nor slow down appreciably, it has too much mass.