Gnargenox:  You cannot build a perpetual motion machine.  No matter how clever the methods you use.   But we can use your questions to understand more about black holes and how energy, and energy conversion, works near them.  

You can extract useful energy from matter falling into a black hole, or from the black hole itself (especially rotating ones).  The amount of energy you can extract cannot be infinite, however.  It cannot be greater than the total mass-energy the system (black hole + whatever you have around it) had to begin with.

Could I use the force generated from the gravitational pull of a Black Hole that is pulling on a long string, which goes into and feeds the hole, replacing whatever mass is lost from Hawking Radiation, without the need for it to be infinity strong? 

Let's simplify this scenario (don't worry, we won't lose any of the physics, or energy converted!)  

Imagine dropping an object of mass m, from very far away, into a black hole of mass M.  If you do, then the black hole becomes more massive by exactly m.  No more, no less, because the total energy of the object is conserved all along the way.  And you get no useful energy from this because it all went into the black hole.

Now to extract energy.  Let's say you have built a shell of some (incredibly strong) material, and locate it near the event horizon at a radius r_o.  On the shell is some device which catches the falling mass and brings it to rest, converting all of its energy of motion into useful energy.  That could then be used to power a laser, beaming the energy back up to a safe distance to be captured and used as you see fit.  We'll assume this whole process of capturing the kinetic energy and beaming it back by laser is 100% efficient.  How much energy could you extract by this process?

According to general relativity, when that mass is brought to rest on that shell, an observer on that shell will measure its mass to be



This is less than the original mass m.  The difference, multiplied by c², was the energy released by bringing it to rest.  We capture it and then beam it back to us by laser.

Now we must consider the gravitation yet again.  The same gravitational field that accelerated the mass (converting potential energy into kinetic if we think in Newtonian terms) is redshifting the laser light as it climbs away from the black hole.  The photons decrease in energy by the same factor that the energy of the object increased (according to observers on shells measuring it locally as it passes them).  Gravity is a conservative force!  Furthermore, the pulse of laser light will take a very long time to reach us, due to the gravitational time dilation.

To maximize the amount of energy converted and beamed back to us, we must build the shell and energy converter very close to the event horizon.  In that limit, the photons are redshifted to infinity, the time it takes for the pulse of laser light to reach us is infinite, and the total energy we receive (over that infinite time!) is exactly equal to the total energy (mc²) of the object we dropped in.  In fact the time is not really infinite, but equal to the evaporation time of the black hole.  Basically we've done no better than turning the object to Hawking radiation, which is exactly what would happen if we had not bothered to capture and convert the energy at all and instead just let the object fall freely into the event horizon!

By the way, this is the best we can do -- the maximum energy conversion we can possibly have from a non-rotating black hole.  Which should make sense from physical laws. 

Here's the fraction of the rest mass we can get, as a function of the radius from the black hole that we build the shell/converter.  This curve is completely independent of the mass of the black hole.

[center][/center]

Can we make a piezoelectric string large enough it wont snap?

No.  Any real string or rope lowered slowly into a black hole will quickly cease to be one, due to the tension which will trend to infinity near the horizon.  Why?  Because of the (locally measured) gravitational acceleration near the horizon.  This acceleration is similar to the Newtonian formula, but divided by a factor of (1-r/r_s)^1/2 due to general relativity, where r_s is the event horizon radius.  The acceleration trends to infinity at the event horizon, but how quickly it trends to infinity depends on the mass of the black hole.  For more massive black holes it increases more gently.  Here it is for the black hole SgrA* at the center of our galaxy:

[center][/center]

[left]If the idea of the locally measured acceleration trending to infinity feels weird, then it is at least consistent with another property of the motion at the event horizon: all observers located on the event horizon will observe all objects falling into the horizon to have a velocity of exactly c, regardless of how far away from the black hole they were dropped!  (Of course no observer can actually hover on the horizon, but we can imagine this as a sort of limit that they are exceedingly close to the horizon.  It also means the observer must be moving at the speed of light to hover on the horizon, which again requires infinite acceleration for anything with mass.)[/left]

[left]

 I guess from our point of view, it never even actually passes over the Event Horizon, so our limit to tensile strength doesn't need to be infinite as well.

We'll say it never crosses the horizon, true, but it does approach the horizon so quickly from our point of view that it makes no practical difference.  If you lower the string in, the tension in it will increase very dramatically, and then more and more of it will become irrecoverable.  Pull the string back up, and the end of it will be missing.[/left]

[left]

This is kinetic energy, the acceleration of the string as it reaches the event horizon. This should not be converted to mass in the Black Hole

[/left]
Incorrect.  If we take an object and drop it into a black hole from far away, then we add more mass to the black hole than if we slowly lowered it down to just above the event horizon and then dropped it in.

In fact there is no generalized sense of distinguishing the potential energy, kinetic energy, and rest-mass energy of an object falling into a black hole.  Different observers will have different notions about what these energies are and how they are converted.  What is true for all observers is that the total energy remains constant for an object freely falling in.

Is this mass that leaves the end of the string actually happening in real time? Is the energy actually lost to the dilation of time?

What do you mean by happening in real time?  What do you mean by mass leaving the end of the string?  

What you are doing is converting mass to energy.  In the Newtonian terms, it is gravitational potential energy converted into... whatever you want to convert it to.  

For an analogy, water spilling over a cliff also converts gravitational potential energy into kinetic energy as it descends.  Then that kinetic energy is converted into sound and some heat when it hits the bottom.  The mass of the water does decrease by this.  Where did it go?  Converted to other forms of energy.  Is time dilation involved?  You can think of it that way if you like, since time passes more slowly at the bottom of the falls than at the top.  But the falling water, or a person going over the falls themself, would have no notion of time slowing down.

Wat, either way, it's not possible to extract more energy from a black hole than from mutual annihilation of matter-antimatter is it?  Or can a black hole drive actually be built to warp space-time and enable speeds faster than are conventionally possible?  Assuming we have the technology to harness that much energy one day.

Wat, either way, it's not possible to extract more energy from a black hole than from mutual annihilation of matter-antimatter is it?

That's right.

Or can a black hole drive actually be built to warp space-time and enable speeds faster than are conventionally possible?

Probably not right.  

There is a sense in which your speed when you have fallen within the event horizon is faster than the speed of light.  After all, observers hovering very near the horizon say your speed is exactly c as you cross it, and surely you must keep speeding up as you fall deeper, right?  Indeed you do!  But nobody directly measures such a faster-than-light speed.  You will always be outpaced by a photon falling in with you, by exactly c, and observers outside the horizon never see you cross the horizon.  Observers inside the horizon cannot themselves be stationary with respect to the black hole, either.  



Aside:  Given that this physics of mass-energy conversion is not unique to black holes but rather a very general kind of thing: how much does your mass decrease, if you reduce your altitude by 1 kilometer on Earth?

The gravitational potential energy on Earth's surface is well approximated by U=mgz where z is your altitude and g is the local gravitational acceleration which we can also approximate as constant. Then if you freefall 1km (and ignore air resistance), you will convert about 9800 joules per kilogram of body mass to kinetic energy.  But let's say you decrease you altitude slowly (say by walking or driving).  Then this potential energy is converted, ultimately, to heat.  What fraction of your total mass was lost by this conversion?  

About 1.09x10^-13.  If you weigh 60kg, that's a bit more than 6 nanograms.  From where?  Did you lose any atoms?  Not for this reason.  But work was done to drop your altitude and keep you at rest with respect to the surface at the end (negating what would have been a gain of kinetic energy).  Energy was expended to do that, and energy is mass.

The total mass of Earth and you together did not change, provided none of the heat was radiated to space.

Gnargenox:  You cannot build a perpetual motion machine.

Oh no! That's so depressing. I had to take a moment to realize all my theoretical work on breaking the laws of physics is down the drain! Sigh.

My mind was just wondering if there are infinities involved there should be some method to piggy-back on something that is infinte and extract a small portion of its infinite energy, or mass or something. i suppose all the methods of interacting with infinities also requires something infinite in itself.

Rather than dropping something straight into a black hole, couldn't we aim to miss it but still gain energy just like sling-shotting a space craft around Jupiter? Maybe it could just be a laser bouncing between mirrors on either side of the black hole? I don't know if this would change the mass or evaporation rate of a stationary (or Schwartzchild?) Black Hole.

But again you cannot get out more than the rest mass of whatever you drop into the black hole.

I guess I don't mind using the energy I get with the string method, to manufacture more string, as long as that doesn't require more energy than I efficiently capture. I thought it might be easy and more efficient than nuclear fusion or fission, and no need for radioactive materials.

I only mention time because it is apart of the equation. I don't know what that equation is but you say :

Gravity is a conservative force!  Furthermore, the pulse of laser light will take a very long time to reach us, due to the gravitational time dilation.

So it is somewhere in there. When I say lost to the dilation of time I guess I mean it wont make it back to us until an infinite amount of time has passed or the evaporation time as you mention.

Basically we've done no better than turning the object to Hawking radiation,

That's fine I guess, if we can suck up the Hawking Radiation and use it somehow lol

all observers located on the event horizon will observe all objects falling into the horizon to have a velocity of exactly c,

Now the violet stars and skies I see in Space Engine while camping on the surface of a black hole makes sense!

Well, I think what you've all said makes sense but it made my head warmer. I guess I will move on to my other thought experiment of what would a graph of my light cones look like if time stopped in a 10 foot sphere around me. Thanks as always Mr Watsisname! You rock!

You can extract useful energy from matter falling into a black hole, or from the black hole itself (especially rotating ones).  The amount of energy you can extract cannot be infinite, however.  It cannot be greater than the total mass-energy the system (black hole + whatever you have around it) had to begin with.

Is this related to the concept of the man-made Kugelblitz 'microblack-holes', which are theoretically useful for energy-production and possibly star-ship drives?

theoretically useful for energy-production and possibly star-ship drives?

That sounds more feasible than my Antimatter Spacecraft using Bananas as a fuel source.

You can extract useful energy from matter falling into a black hole, or from the black hole itself (especially rotating ones).  The amount of energy you can extract cannot be infinite, however.  It cannot be greater than the total mass-energy the system (black hole + whatever you have around it) had to begin with.

Is this related to the concept of the man-made Kugelblitz 'microblack-holes', which are theoretically useful for energy-production and possibly star-ship drives?

Yes this is what I was asking Wat about.  Asimov actually used this method to power the AI spaceship in the (chronologically) last two books of the Foundation series (written in the 80s).

Thanks Wat, sounds like we could still have a black hole drive but it wouldn't be capable of superluminal velocities the way the Alcubierre drive would (still very theoretical.)

Oh no, more questions come to mind after reading about Dark Energy and Dark Matter being the same thing.

Negative mass, hmm, is Hawking Radiation something like antimatter, or it is some negative mass particle created when the other half of an entangled pair of atoms get too close to the event horizon, when the particle with mass falls in and a negative mass particle escapes?

Or why not both? Both antimatter and matter have positive and negative mass particles, black holes eating all the ones with positive mass and Hawking radiation being both matter and antimatter negative mass particles, but now don't annihilate one another?

Can we just rule out negative mass particles and make things easier?

That sounds more feasible than my Antimatter Spacecraft using using Bananas as a fuel source

Haha! Yeah, I remember reading your post about that. It's pretty neat. It reminds me of one of those classical engineering challenges: "Well class, how can we make a spaceprobe operable by chimps?"

Yes this is what I was asking Wat about.  Asimov actually used this method to power the AI spaceship in the (chronologically) last two books of the Foundation series (written in the 80s).

Yes, it's an old concept. The difference between Kugelblitz holes and and natural blackholes is that they are much smaller -  microscopic even and comparatively shorter lived.

is Hawking Radiation something like antimatter

It is related to antimatter or negative mass by virtue of it's mathematical properties. It is a black-body radiation emitted by the event-horizon of the blackhole, not quite the hole itself (since nothing can be emitted by it obviously, like light photons or even electromagnetic forces). Stephen Hawking theorized that because gravity has an unknown quality in relation to quantum mechanics, this allows gravitational effects to be weak enough for calculations in the framework of quantum field theory in curved spacetime to be performed. This could allow quantum effects to create black-body radiation being emitted by the event horizon. Blackbody radiation temperature is inversely proportional to the mass of the blackhole. Virtual particles are boosted by the black hole's gravitation into becoming real particles. A particle–antiparticle pair is produced by the black hole's gravitational energy, and the escape of one of the particles lowers the mass of the black hole. The escaped particle is Hawking Radiation. Mind you, this is theoretical.

An alternative view is that these particle pairs are produced by vacuum fluctuations and that as one particle falls into the hole, in order to preserve energy, the infalling particle has to have negative mass. This causes the blackhole to loose mass, a process that to an outside observer appear like the blackhole released a particle.

Kugelblitz blackholes release more Hawking radiation then natural ones, and thus they could be used as a power source, if Hawking radiation exists, of course.

That was such a good explanation that I understood at least half of it!

Another property of the Hawking radiation is that its source cannot be localized, as in we cannot say it is coming from the event horizon.  As Stellarator said it is a radiation with the spectrum of a blackbody, so the black hole is emitting photons as if it has a temperature.  The temperature is inversely proportional to the mass of the black hole, and the peak wavelength of the radiation is several (about 8) times the diameter of the black hole.  So if you could make an image of a black hole by its Hawking radiation, it would look very fuzzy.

It's worth pointing out just how weak this radiation is for typical (stellar mass or supermassive) size black holes.  Consider SgrA* at our galactic center with a mass of about 4 million Suns.  The effective temperature of this black hole is 1.5x10^-14 Kelvin, radiating 5.6x10^-42 Watts, with a peak wavelength of 1.3AU (!).  On average, it emits 170 photons of Hawking radiation per year.  

It's also interesting to connect this back to your idea of energy extraction from black holes.  As we discussed, large fractions (approaching 100%) of the rest mass of an object can be converted into energy and harvested.  But the closer to 100% conversion we want to get, then the closer to the horizon the conversion must occur, and the longer it takes for the energy to be extracted out to large distances.  The rate of power extracted plummets, and the wavelength (if converted to light) blows up.  So it looks more and more like we are simply converting the object to Hawking radiation.  Why?  This is actually a very interesting piece of insight to the properties of a black hole.  If you hover close to the event horizon, then distant observers will say you are fried by Hawking radiation!

This is closely related to Unruh radiation, described here on PBS SpaceTime:

[youtube]7cj6oiFDEXc[/youtube]

One way to think about this is that according to those faraway observers you stuck around near the black hole for a very long time, as it evaporates.  But due to the time dilation effect this all took place in a short time as measured by you.  So you experience a lot of Hawking radiation very quickly -- the vacuum around the black hole must be seething with it.  But if you instead fall freely into the hole, then no such furnace of Hawking radiation cooks you.  

Weird, eh?

Rather than dropping something straight into a black hole, couldn't we aim to miss it but still gain energy just like sling-shotting a space craft around Jupiter? Maybe it could just be a laser bouncing between mirrors on either side of the black hole? I don't know if this would change the mass or evaporation rate of a stationary (or Schwartzchild?) Black Hole.

If it's a nonspinning black hole, then we won't get any useful energy extraction this way.  The laser will lose the same amount of energy as it moves away from the black hole as it gains as it moves toward it on each bounce (this is what we mean by the gravitational field being "conservative" -- the net change in energy over any closed path is zero).  

That's true for a slingshot of a planet as well.  If you are in orbit around Earth and try to "sling" around it, you won't gain any energy.  You just continue the ellipse.  What makes an interplanetary slingshot or gravitational assist work is when you start in orbit around the Sun, then pass near a planet that is also orbiting the Sun.  The encounter transfers some of the planet's orbital energy to you, changing your orbital energy with respect to the Sun while your orbital energy relative to the planet is unchanged.  You can think of it as being like a perfectly elastic collision, except without direct contact.  

Shooting a laser near a spinning black hole could net you a gain in energy, however.  This takes advantage of the ergoregion around the black hole, transferring some of the black hole's spin to the energy of the light in a process called superradiance.  This is also the idea behind a "black hole bomb", using light and a specially constructed mirror to extract rotational energy from a spinning black hole and produce an explosion of tremendous power.  A black hole's spin can also be harvested (less destructively) by the Penrose Process, where some mass is sacrificed to the black hole so that the remainder gets flung away with more energy than it started with.  The difference came from the rotation of the black hole, reducing its spin a little.  Kind of similar to a gravitational slingshot, which shrinks the orbit of the planet slightly to account for the boost relative to the Sun.

Now the violet stars and skies I see in Space Engine while camping on the surface of a black hole makes sense!

   It's a crazy view, isn't it?  Some insights (and visualizations) for this effect can be found again on Andrew Hamilton's website (dang do I reference that guy a lot).  The basic idea is that of relativistic beaming.  To hover near the black hole's horizon, you must accelerate like a fish swimming madly on the edge of a waterfall -- in this case a waterfall of space itself.  So you experience an intensified flood of starlight sweeping past you, blueshifted to higher energy.  The acceleration also distorts your field of view, compressing the view of the outside universe to a small disk above you.  In the limit that you hover right on the horizon, this disk shrinks to zero size with infinite brightness.


Some formulas for black holes and Hawking radiation:

Effective radiation temperature (as measured from far away)


Power emitted can be found by the Stefan-Boltzmann law for a surface with the area of the event horizon and its effective temperature:


Peak wavelength can be computed from Wien's Displacement Law.

Rate of photons emitted can be found by relation of energy to wavelength:

(Then divide the power emitted by the energy per photon of that peak wavelength).

This is also the idea behind a "black hole bomb", using light and a specially constructed mirror to extract rotational energy from a spinning black hole and produce an explosion of tremendous power.

Ahh yes, Roger Penrose. A few years ago I read his work after coming across it so often. His writings on superscalar weaponry is indeed frightening. Have you heard of his theory of the Thunderbolt, a gravitational wave of singularities that can rip through the entire universe? Scary stuff that, though of course completely impossible and unfeasible to engineer.

That sounds more feasible than my Antimatter Spacecraft using using Bananas as a fuel source

Haha! Yeah, I remember reading your post about that. It's pretty neat. It reminds me of one of those classical engineering challenges: "Well class, how can we make a spaceprobe operable by chimps?"

Yes this is what I was asking Wat about.  Asimov actually used this method to power the AI spaceship in the (chronologically) last two books of the Foundation series (written in the 80s).

Yes, it's an old concept. The difference between Kugelblitz holes and and natural blackholes is that they are much smaller -  microscopic even and comparatively shorter lived.

is Hawking Radiation something like antimatter

It is related to antimatter or negative mass by virtue of it's mathematical properties. It is a black-body radiation emitted by the event-horizon of the blackhole, not quite the hole itself (since nothing can be emitted by it obviously, like light photons or even electromagnetic forces). Stephen Hawking theorized that because gravity has an unknown quality in relation to quantum mechanics, this allows gravitational effects to be weak enough for calculations in the framework of quantum field theory in curved spacetime to be performed. This could allow quantum effects to create black-body radiation being emitted by the event horizon. Blackbody radiation temperature is inversely proportional to the mass of the blackhole. Virtual particles are boosted by the black hole's gravitation into becoming real particles. A particle–antiparticle pair is produced by the black hole's gravitational energy, and the escape of one of the particles lowers the mass of the black hole. The escaped particle is Hawking Radiation. Mind you, this is theoretical.

An alternative view is that these particle pairs are produced by vacuum fluctuations and that as one particle falls into the hole, in order to preserve energy, the infalling particle has to have negative mass. This causes the blackhole to loose mass, a process that to an outside observer appear like the blackhole released a particle.

Kugelblitz blackholes release more Hawking radiation then natural ones, and thus they could be used as a power source, if Hawking radiation exists, of course.

I would love for negative and/or imaginary mass particles to exist, we could do so many neat things with them   One of the ideas about virtual particles is that the Law of Conservation of Mass-Energy applies over a whole multiverse/omniverse so what disappears from one universe reappears in another and vice versa, and this could be through tunneling thru quantum foam (which would really be microblackhole-wormhole pairs.)

Looks like you're a big fan of Andrew Hamilton, Wat!  You like him the same way I like Michio Kaku, though I love Andrew's clear explanations also!

What you said here

Shooting a laser near a spinning black hole could net you a gain in energy, however.  This takes advantage of the ergoregion around the black hole, transferring some of the black hole's spin to the energy of the light in a process called superradiance.  This is also the idea behind a "black hole bomb", using light and a specially constructed mirror to extract rotational energy from a spinning black hole and produce an explosion of tremendous power.  A black hole's spin can also be harvested (less destructively) by the Penrose Process, where some mass is sacrificed to the black hole so that the remainder gets flung away with more energy than it started with.  The difference came from the rotation of the black hole, reducing its spin a little.  Kind of similar to a gravitational slingshot, which shrinks the orbit of the planet slightly to account for the boost relative to the Sun.

Still retains the same amount of total energy no? It's just that some of the energy from the black hole is transferred to a moving object?

I was confused by the surface of black hole thing, I thought black holes dont have surfaces?  They are a region of space-time rather than an actual object right (the actual object got crushed into a singularity.)  I've never seen the kind of view that was talked about.

It's almost like others see a shadow of you (not a clone) that was trapped at the event horizon.
Also, I have a completely unrelated question (actually two):

Is life possible in a system with a black hole in it, provided the planet is far enough away from the black hole to avoid its tidal effects and that the planet developed after the black hole was created?

Also, is life possible on planets orbiting O and B or even Wolf-Rayet type stars? I see many procedural planets around stars of these types, but we haven't discovered any real planets orbiting a blue star have we? The skies would look spectacular!  Even though the lifetimes of these stars are relatively short I was wondering if life could still develop on them, through accelerated evolution and perhaps if the planet's atmosphere could shelter the surface from UV light (or possibly underground or underwater life- as long as the planet is far enough away from the parent star to have liquid water.)

Thinking negatively, is Dark Matter just static electricity? Created by the gravitational pull and spin created by normal matter coalescing on a galactic scale, does this create an electric charge, negatively, in the center that radiates out, giving the center a positive charge? The outer regions have a negative charge and are pulled inwards? We could test this flow of these free protons somehow, knowing the steady state charge of stars or planets, maybe. Or maybe their galactic orbits. So, galaxies would be kinda like magnets, and if they collide would have very odd patterns of matter vs dark matter like the Bullet Cluster.

Oh, I guess I need to understand magnets a little better. Its the only thing that looks like gravity other than acceleration, but its electrically driven. I guess magnetic fields stretch as far as gravity does too. But every time I get a change to ask Richard Feynman "Why do magnets work?", he starts punching the wall and says "Why do pencils in a box of ping pong balls always point in only 1 of 6 directions?", never really explaining to me why magnets work.

Still retains the same amount of total energy no? It's just that some of the energy from the black hole is transferred to a moving object?

That's right.  This process extracts the angular momentum of the black hole.  If we extract everything we can, then we'll be left with a a nonspinning Schwarzschild black hole.

I was confused by the surface of black hole thing, I thought black holes dont have surfaces? 

By a black hole's surface we mean its event horizon, which is a surface in space-time.  This has a unique location and surface area which everyone agrees on, and a powerful geometric meaning.  Any observer who crosses the event horizon cannot escape again (it is an absolute one-way surface).  All events that transpire within the event horizon can never be known to outside observers.  

If you fall through the event horizon yourself, then passing through it is an uninteresting experience.  There is no physical sensation, or even an obvious visual cue, as to when you crossed it.  After crossing it you still see the outside universe, and the black disk of the hole still appears to be in front of you.  But you are in the black hole's interior and now doomed to hit the singularity.

It's almost like others see a shadow of you (not a clone) that was trapped at the event horizon.

Sort of.  What they see (not really since the image very quickly becomes redshifted to infrared, radio, and then complete invisibility) is light that you emitted just before you crossed the horizon in your frame of reference.  Your passage through the horizon took place in finite time, so the amount of light you emit is finite, and the time dilation or gravitational field stretches the time it takes for that light to escape to the distant observers to infinity.  So they see an ever-fading image of you.

Is life possible in a system with a black hole in it, provided the planet is far enough away from the black hole to avoid its tidal effects and that the planet developed after the black hole was created?

Certainly!  Far from a black hole we can still have perfectly well behaved orbits.  If planets survive the supernova of a star that formed the black hole, then it might not be hard to imagine life surviving for a while in the warm interior of the planet (lithotrophs for example).  There is also no principle of physics that would prevent an advanced space-faring race from inhabiting such a black-hole-orbiting planet, or putting a habitable planet there.  They could also take an isolated black hole and give it just the right accretion rate to produce enough light to make it act like a Sun, providing light and warmth to planets around it.

Also, is life possible on planets orbiting O and B or even Wolf-Rayet type stars? 

Probably unlikely, since these stars have very short main sequence life-times, making it difficult for life to evolve around them.  They also give out a much higher proportion of ultraviolet light compared to cooler stars.