Relativity and Cosmology Blog

# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

 Previous in Blog: Gravity Probe B and Frame Dragging Next in Blog: Extreme Frame Dragging

# GIGO: Garbage In, Gigawatts Out?

Posted April 01, 2007 11:00 PM by Jorrie
Pathfinder Tags: black hole Free energy

It's a dream of many people: free energy, cars running on water, vacuum energy, over-unity machines, etc. Here's a dream that may (perhaps) one day come true. If we can find a rotating black hole within reachable distance and with a hospitable environment around its equator, we can colonize that space and have clean "free" energy for our colony!

Pictured below is a design based on Sir Roger Penrose's black hole energy extraction process. It shows a mega-city built on a rigid structure around the equator of a massive, spinning black hole. The city is at just the right distance from the hole so that the local gravity is at a comfortable 1g and that tidal forces and inertial frame dragging do not affect the structures adversely.

Figure 1:

Credit: Gravitation, Misner, Thorne, Wheeler (MTW), fig.33.2

The city's garbage is processed at the top left by dumping it into suitable containers and dropping the containers at a carefully chosen angle towards the black hole. Due to frame dragging, the containers swing around the black hole in its ergosphere[1], and so "steal" some of the black hole's angular momentum.

Just before the container starts to leave the ergosphere, the garbage is ejected towards the hole, to be "swallowed" by it. Due to black hole dynamics, the garbage instantly attains negative energy. The negative energy entering the black hole causes its rest mass to decrease. At the same time, the "lost" energy (or most of it) is added to the container as kinetic energy.

The result is that the empty container recoils outward with enormous velocity. The increased spacing of the small square blocks in the graphic indicate the relatively large outgoing speed. For a suitable ratio of garbage to container mass, the outgoing speed can be a large fraction of the local speed of light! This sort of thing is observed in nature when a star (one part of a binary system) is flung out of the center of a galaxy at a speed approaching the speed of light.

At the city's power station (top), the high-speed container is caught in a suitable water wheel-like machine that dumps most of the empty container's huge kinetic energy into the rotation of a flywheel. This flywheel powers a generator, feeding the city's electricity grid. The empty container is then reused for another load of garbage.

As stated in the authoritative MTW and mathematically shown by Penrose, if optimally executed, the net energy gain of every container's round trip approaches the total rest energy (E=mc2) of the garbage ejected, plus some fraction of the considerable angular momentum of the rotating black hole. Think about the benefits:

(i) Garbage completely out of sight, hidden by an event horizon.

(ii) Nearly 100% of the mass-energy of the garbage is turned into usable electricity.

(iii) Some of the black hole's spin energy is thrown into the mix as well.

If this does not qualify for "over-unity", I don't know what will!

Regards, Jorrie

PS: This futuristic power station can produce around one gigawatt-hour of electric energy for every metric ton of garbage dumped into it. What a pleasure!

Oh, I can already hear the "green party" of the city raising at least three issues here:

(i) We are polluting the black hole's singularity.

(ii) We are "burning" the black hole's mass (if they can figure this one out!)

(iii) Why do citizens have to pay for garbage removal and for the "free" electricity?

[1] For the ergosphere, see http://cr4.globalspec.com/blogentry/1372/Rotating-Black-Holes-the-Naked-Truth

-J

Interested in this topic? By joining CR4 you can "subscribe" to
Guru

Join Date: Sep 2006
Location: Auckland, New Zealand
Posts: 8778
#1

### Re: GIGO: Garbage In, Gigawatts Out?

04/02/2007 12:17 AM

Ignoring the fact that black hole physics, negative energy, and well just about every theory regarding black holes has yet to be proven (or for that matter be agreed upon), I fail to see how this sort of structure could possibly ever get even close to breaking even when all factors are taken into account, for example - the vast resources required to make such a structure, or how about even the fuel energy required to get the materials to the black hole. It just could not be made practical.

There is no free lunch, and getting someone else to pay for said lunch does not make it free (i.e. someone still has to pay for it).

__________________
Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#2

### Re: GIGO: Garbage In, Gigawatts Out?

04/02/2007 1:09 PM

Hi Jack, agreed, but it's fun to speculate - how about mining the resources from a handy planet in the vicinity?

One can then ask, why not just colonize the planet? Problem is, us humans will pollute it so much in time that we'll have to keep on looking for new planets to "cannibalize".

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Power-User

Join Date: Feb 2007
Posts: 158
#3

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 12:10 AM

BOY; Every body keeps telling me running a car on free energy or Hydrogen can't be done. Free energy ,running cars on water, and over unity have been or are being, and or will be done long before this pipe dream ever takes off. If they're not being done then somebody isn't paying attention to the things that need to be done here and now. The designers of this pipe dream would do well to come back down to earth and do something constructive in this relm.

Commentator

Join Date: Feb 2007
Posts: 73
#4

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 6:00 AM

The only thing holding us all back from most of our pipe dreams isn't energy production, it's energy storage! We got all kinds of ways of generating energy but we are seriously lacking in the storage department. The best energy storage technologies we have so far are all chemical devices but the nulcei of atoms can hold far more energy than their electron orbitals. A real energy storage breakthrough would be to find a safe and reliable way of pumping large amounts of energy into atomic nuclei and then retrieving the energy as needed. I'm not talking about anything as extreme as nuclear fission or fussion here. We have atomic battery technology but, it's not practical. Maybe some kind of microchip scale nuclear magnetic resonance (NMR) technology would do the trick. I mean, if we could do this then every electrical device in the world could contain it's own lifetime power supply. Even better would be an all-purpose battery that could power anything from your cell phone to your power tools to your electric car. You could keep it on your key chain and take it with you wherever your go. It would be kind of hard to steal someones car when they've got the "gas tank" in their pocket or purse.

Associate

Join Date: Mar 2007
Location: Western NY
Posts: 31
#5

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 8:41 AM

My knowledge of black holes is pretty basic. How "big" is this theoretical black hole (golf ball? Jupiter? Sun?). How "big" would the city have to be to be at 1g gravity? I guess this question is similar to the "how much resources" would be required to build this city. Also, I thought that the black hole would consume the garabage, not catapult it, and then get bigger and then bye bye city. It is an interesting thought though.

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#14

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 11:27 PM

hi Worden, you wrote: "Also, I thought that the black hole would consume the garbage, not catapult it, and then get bigger and then bye bye city."

The idea is indeed that the garbage is consumed - it's only the empty container that goes back with the extra energy. The other "funny" is that although the black hole consumes the garbage, it gets smaller/lighter because some of its mass is converted to energy!

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Commentator

Join Date: Feb 2007
Posts: 73
#6

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 12:49 PM

The only black holes I know of are the ones that live in the centers of gallaxies. They aren't just wondering about between the stars. That city might then be as big as the "central bulg" of the Milky Way so, it definitely would not be a solid structure as depicted in the cartoon but a Dyson Ring (http://en.wikipedia.org/wiki/Dyson_sphere#Dyson_swarm) of titanic plateforms orbiting the black hole some distance appart from each other. As such, much of the energy derived from the black hole (by whatever means) would need to be used to generate a constant thrust below each platform for gravity.

As I understand it, matter and energy naturally "evaporate" from above the event horizon of black holes. That alone might yield enough energy for us. If not, we could try tapping the two massive jets of particles that naturally spew from the poles. Regardless, by the time we R&D our tech far enough to build such things, there will likely be no such thing as garbage. Indeed, 100% recycling will likely be an essencial prerequisite of such an undertaking. For example, we might need to mine materials from commets, asteroids, moons and small planets to build huge colonial star ships, fly the ships to the black hole and then recycle the ships to build the platforms.

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#7

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 2:48 PM

Hi Harbinger, you wrote: "The only black holes I know of are the ones that live in the centers of galaxies. They aren't just wondering about between the stars."

Theoretically, the most common (plausible and usable) type of black holes are the ones "wandering about between the stars". They come from supernovae, where the mass of the collapsing star is from a few tens to a few thousand solar masses. There are more supernovae than there are galaxies which could harbour super-massive black holes in their centers.

It's these "smallish" black holes that may have "hospitable" environments. The smallest black hole that can theoretically exist, after a star has gone supernova, is 1.44 solar masses. At this mass, the mega-city must be at ~4.4 million km from the black hole to enjoy 1g of static gravity (r = sqrt[GM/9.8]).

How "mega" must the city (or at least the girder-work keeping it up) be? Well it will have to be about 28 million km in circumference. Ouch! One can make the circumference smaller by getting closer to the hole and let the whole structure rotate around the hole. It cannot be in normal orbit though, because that will cause weightlessness - probably not good for humans...

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Anonymous Poster
#8

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 5:28 PM

I understand that black holes spew out massive amounts of radiation - X rays and so on. Setting up home anywhere near a black hole would be highly dangerous to human health and we may all end up as deformed mutants in a few generations. The "free lunch" would come with a huge price tag that doesnt sound worth it to me.

Ecologist, writing from a save corner of the Galaxy

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#10

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 1:30 AM

Hi Guest, you wrote: "I understand that black holes spew out massive amounts of radiation - X rays and so on."

It is only black holes that are still in their "feeding stage" that spew out massive radiation. It comes from gas, dust, planets, stars, etc. that form an accretion disk around the black hole's equator. The high-energy rays happen when the matter is so compressed that the temperature reaches extremely high temperatures.

Once the neighborhood is swept clean and other matter orbit at safe distances, this "feeding frenzy" stops and the environment is most probably no worse than in other piece of free space. However, the colony should be well shielded, like any long duration spacecraft containing humans.

About the other "implausibilities", as Emjay4119 named it below, well, they are at least based on solid science, whatever that may mean...

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Guru

Join Date: Dec 2005
Location: Queensland Coalfields Australia.
Posts: 697
#11

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 1:50 AM

I'm thinking the building phase will be a nice little challenge at least until the ring is closed to balance the gravitational effects.

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#12

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 4:30 AM

Hi Emjay4119, yes, a "nice little challenge"!

One way is to construct it far from the black hole and then slowly "rocket" the whole structure into place. Another is to first build the pieces in orbit around the hole and then steer each subsystem by a propulsion system to its "static" position.

Any other ideas?

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran
Guru

Join Date: Dec 2005
Location: Queensland Coalfields Australia.
Posts: 697
#9

### Re: GIGO: Garbage In, Gigawatts Out?

04/03/2007 9:17 PM

I've been thinking the only way to control the Perpetua threads was to use the same method as controlling rumours. If you haven't heard a good one by 10.00am, start one. Well done Jorrie, you must have read my mind. At least this one is interesting and has a whole new range of implausibilities to explore. You'll be able to build it right after you bring John Bradfield back from the dead.

Anonymous Poster
#13

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 9:12 PM

Anonymous Poster
#15

### Re: GIGO: Garbage In, Gigawatts Out?

04/04/2007 11:49 PM

Jorrie, after all the diversions, back to the science.

If the garbage is fully converted into energy by E=mc2 and added to the container's kinetic energy, while the black hole's mass decreases by that same amount, I fail to see how the conservation of mass-energy is satisfied.

Lets say we start with energy E1 = mc2 + Mc2, where m is the mass of the garbage and M the mass of the black hole. The kinetic energy of the container is initially zero. After the conversion, we have:

E2 = 0 + (M-m)c2 + mc2, where the zero is for the now vanished garbage and the final mc2 is for that energy converted to kinetic energy of the container, giving

E = (M - m + m)c2

= Mc2 < E1

So, the universe has just lost mc2 in mass-energy. Or is it me that is missing something?

SL

Guru

Join Date: May 2006
Location: 34.02S, 22.82E
Posts: 3817
#16

### Re: GIGO: Garbage In, Gigawatts Out?

04/05/2007 3:27 AM

Hi SL, you wrote:

"E2 = 0 + (M-m)c2 + mc2, where the zero is for the now vanished garbage and the final mc2 is for that energy converted to kinetic energy of the container, giving

E = (M - m + m)c2

= Mc2 < E1"

Maybe I have stated things slightly conservatively. The actual final raw kinetic energy gain is double the mass energy of the garbage (2mc2), but obviously all of that cannot be converted into usable electricity. The (perhaps even optimistic) guess is that an advanced civilization may get a 50% yield out of that, i.e., mc2.

MTW states it as follows:

"As the garbage flies down the hole, changing the hole's total mass-energy by Egarbage ejected < 0..." and

"(Energy gain per trip) = (rest mass of garbage) + (amount, -ΔM, by which the hole's mass decreases)"

I read this as equaling 2mc2, because ΔM = -mc2, per the above MTW definition. Note that MTW works in units where c = 1, hence mass and energy are in the same units.

E2 = 0 + (M-m)c2 + 2mc2 = (M+m)c2 = E1 in your definition, so no lost energy.

Regards, Jorrie

__________________
"Perplexity is the beginning of knowledge." -- Kahlil Gibran