5
$\begingroup$

Say you were using a black hole as a propulsion drive á la Crane and Westmoreland http://arxiv.org/pdf/0908.1803.pdf- so your black hole has a radius of around .9 attometers - super tiny - around 600,000 tonnes. How much energy would be required to increase its size to say 100 earth masses? And how quickly could you do it? Is there any way that much energy could be contained in a bomb or weapon? Crane and Westmoreland talk about using spherical gamma lasers to create their artificial black holes. Is there a possible solution here? We are obviously talking about advanced technology, but if it's just too absurd, I want to know.

$\endgroup$
  • 2
    $\begingroup$ You've asked a couple questions about black holes recently, but none of them seem very researched to me at all. I'd suggest doing more research before asking these questions. Also, to me they read as pure physics questions, and as such unsuitable for this site. Perhaps some more in depth research before asking would shed some light on your questions. $\endgroup$ – Aify Mar 30 '16 at 4:45
  • 3
    $\begingroup$ @Aify Concluding insufficient research is a tad harsh IMHO. There's a link to arxiv, which suggests that some effort was made to understand concepts involved, but considering that many who may have an interest in such topics may not have such a background, terminology/arcane math is often a barrier to learning. Secondly, the question is framed around an interest in developing a concept of warp drive which is purely speculative, and as such, I would consider this an acceptable form of question here. Furthermore, good science is hard to come by and encouragement is a plus. Point taken N-T-L. :) $\endgroup$ – Nolo Mar 30 '16 at 6:46
  • 1
    $\begingroup$ Well... you could increase the mass of a black hole (or any object, for that matter) by simply throwing stuff at it, provided the stuff you throw is substantially smaller than the object. Gravity will make them stick, increasing the mass. $\endgroup$ – Burki Mar 30 '16 at 10:51
  • $\begingroup$ @Nolo Before concluding insufficient research, I went and tried to google the topic and his questions, and found sufficient answers to them similar to the links and answers in your own answer. Reading the links from your answer also provide more than enough evidence that he could have simply found and read 2/3 of those links himself, with some googling. The link to arxiv just means he read something interesting - it doesn't show any additional research made. $\endgroup$ – Aify Mar 30 '16 at 14:17
  • $\begingroup$ Furthermore, upon reading deeper into the linked pdf, there is an entire section on "Theoretical Feasibility" (Section IV), which gives numbers and arguments as to what would be required for the idea of the black hole star ship to work; 1000000 tonnes of mass, lifetime of decades to centuries, how to produce it using the sun's energy and solar panels. But everything I've just said is moot because the article goes into even MORE detail regarding the exact numbers OP put in his question. Any more details required would just be calculations that I wouldn't consider worldbuilding. $\endgroup$ – Aify Mar 30 '16 at 14:24
6
$\begingroup$

There are some problems Let say we switched off, Black hole evaporation

I can't correctly explain the details of feeding a black hole, so everything below is roughly speaking.

As stated here Schwarzschild radius

A small mass has an extremely small Schwarzschild radius. A mass similar to Mount Everest(estimate of $6.3715e14$ kg) has a Schwarzschild radius much smaller than a nanometre.

$2 \times\text{ 6.6738e-11 m}^3 \text{kg}^{-1} \text{s}^{-2} \times\text{ 6.3715e14 kg / (299 792 458 m /s}^{-1})2 = \text{9.46e-13 m, or 9.46e-4 nm}$.

Typical atom size is $\text{1.4e-1 nm or 1.4}$ Ångström
Typical nucleus size is $\frac{1}{10000}$ of atom size so let say $\text{1e-5nm}$

So an Everest mass black hole is much less than external atom size and $10-100$ times bigger then nucleus size.

But how big are gravitational effects
at distances 1.4Å form BH
Atoms get a speed increment something like $\text{20000km/s}$ per each 1Å distance traveled at distance 1-2Å from BH Everest. It means if place BH and atom 2Å apart, an atom will gain speed between 20k and 40k km/sec - more likely 25-30 thousand km/s

at distance 1 meter 42522 m/s2
at distance 10 meter 425 m/s2
at distance 100 meter 4 m/s2

If it is solid body
So let say you placed BH in center of mass of some solid body, and BH isn't moving relative to that center.
May you expect the BH will eat a 1 meter hole inside - yes
May you expect the BH will eat a 10 meter hole inside - yes, probably
May you expect the BH will eat a 100 meter hole inside - not necessary, depends on the material, and the surrounding environment. If it is solid rock asteroid probably he will stay, just with some hole inside.
Do not take other factors into account, this situation is stable it's like 2 bodies orbiting one center of mass, just one is inside, as also center mass of that 2 body system.

If it is some gas cloud
Let say something between 10 and 100 meter radius will be compressed gas(because of gravity), and let say it was eaten by BH in instant time, let it be 100 meter radius.
How fast BH will get new materials? The answer mostly depends on Temperature of that surrounding gas. Typical speeds of atoms and molecules in gas like Air we breath equals the speed of sound (so typical in our environment 300-330 m/s, with near room temperatures) Something near that speed will be maximum speed of consumption of that surrounding gas cloud.

In both cases, I'm simplifying, but that is general picture.

Are there some other limiting factors? Yes, they are.

Back to atoms
On the atomic level, near BH at 1Å distances will be some pressure between atoms as they wish to go inside BH bar.
Are they all allowed to go to BH all at once? - no, they don't.
Why? Because of that fact they are big compared to the size of BH.
Do they pressure themselves enough to fuse, and go not as individuals but as a bigger pack? Depends. Even for Everest mass BH, it may be not the case even with Hydrogen Helium3 mix. At some point, it will be possible, but in case of H+He3 to make mix be able to fuse, the speed of atoms should be something close or more than 0.1c. At that speeds, they have a probability to fuse, not granted but possible. But for more heavier atoms(let says C12) this speed must be even more, and heavier they are, more temperature it needs (and the temperature is actually proportional to velocity2)
So fusion around BH is possible at some point and volume where it begins is atom size volume around BH, a volume which all atoms wish to take but they do not fit in to.

Over oversimplifying, but what if they are not speedy enough to fuse. Atoms will bump around the tiny place in space, some lucky atoms will get to BH bar, rest of them will bump each other hard, but not hard enough to fuse. They will be angry and emitting gamma rays, light etc. They will swirl around the BH bar and also they will prevent new individuals to come closer to BH, by dispersing energy and bumps around BH.

No fusion. What it means actually.
It means, theoretically and over oversimplifying, You may place a finite amount of atoms around 1Å sphere around BH. 8 atoms will be enough to seal BH completely. It's like a crystal structure but around some empty and massive point in the universe. It will have some equivalent pressure, high, but not high enough for fusion of that 8 atoms to happen. Some mass limits for such blackhole state may be calculated, take look at neutron stars if you wish, there is something similar in-between.
If there is only 8 atoms and BH and over oversimplification - this situation is stable, stable as BH stable. If we will take BH (by gravity beam I guess) and shake it, nothing will happen with sealing atoms, until we shake less then 2e6 g or 2e7m/s2

How to prevent seal of approval to happening and feed baby BH properly
or Force of Order and Light and over oversimplification

As baby BH have troubles to swallow atoms, you have to feed it one by one. Atom nucleus size BH probably may swallow the only nucleus emitting most electrons, which will form some negative charge around that place, and possible that electron feed rate will be slower then nucleus feed rate, because of some observations that electrons are a particle and wave same time. But that is a dark force of quantum mechanics, which is nearby forbidden darkest knowledge of necromancers about quantum gravitation. But as child's of light and oversimplification we assume baby BH can swallow entry atom.

How to prevent forming 8 atom seal? Here comes Order: we have to feed atoms one by one, and be careful that each atom is eaten before we send next atom.
But also we wish to do it as fast as it's possible - 1c, the speed of the light.
Also, we wish it be dense as much as it possible for us to make, so we leave no space between atoms.

So it will look like fine rope, 1 atom thick, flying at near 1c speed direct to BH.
So for Hydrogen, one atom each 1Å or 1e-10m, or 1e10 atoms each meter - so feed rate will be 3e18 atoms per second or 9.5e25 atoms per year.
Using Avogadro constant ($6.022140857(74)\times 10^{23}\text{ mol}^{−1}$) and pinch of black knowledge:

Feed rate is: 150 Grams of Hydrogen a year. (or 5.29 Oz)

If we take heavier atoms with uranium-238, which is 238 Grams per mole it will be 37.39kg per year (157mol x 238G).
Size of baby BH is linearly proportional to its mass, so to grow Everest like BH by 1 percent we need 42,476,666 million years with Hydrogen and 178,473 million years with U-238.
If we feed it in 10 streams which is more then 8atom seal - and probably is above the limit we can feed baby BH, it's still 17000 millions of years.

Everything is more complicated than that, but bunch factors that are switched off, makes feeding easier and faster. Effects of gravity on such small scale are not known, and it possible they make feeding rate faster or slower. If you wish to answer that question - go study physics.

Some solutions? Yes(kinda).

There at least 2 solutions, that kinda may help with feeding.

First one
Special relativity says to us: $\text{E=mc}^{2}$ and with General relativity, they both say: speed is a mass, mass is a speed, energy is the mass (or something similar, I'm not sure)

So black magic of knowledge and it says: we actually may make Hydrogen atom have more energy by accelerating it for speeds 0.9999999999c and it will have more mass from BH standpoint of view. We can't feed faster than 1c, but we can make atoms have more energy and mass for our BH. Everything depends on how close to light speed we can accelerate our atoms. Some information here relativistic mass.
Roughly speaking it grows like that: $$m = {m_0\over \sqrt{1-\displaystyle{v^2\over c^2}}}$$ So with so much close 0.9999999999c, it will be that much 70710 times heavier, still, millions of years for 1% grow but try harder, feeding baby BH is serious business.

Second option
Most parts of our Universe are too fluffy and not dense enough to grow baby BH fast, but there is at least one possible object that we may feed to baby BH and it maybe will be happy and grow much faster then we can make, at the moment. Probably we may drop BH intoNeutron Star.
That picture amazes me, so I will make boldest question I can:

What will happen if baby BH will be dropper into Neutron Star.

IDK.

It may consume NS, with thunder and lights (gamma rays, bosons, quarks, leptons etc) and will be pretty grown and beautiful Black Hole.
Or it may be still not dense enough, and it will grow definitely faster then we can feed it but still millions of millions of years before it will grow.
Or maybe, and that is what amuses me, it can blow Neutron Star into pieces.
Or it will create sphere of the Light inside that NS, and pressure of that Light will be equivalent to pressure inside Neutron Star 1.6×1035 Pa , and this bubble will grow, and then booom all that energy released, and there are pieces of neutron stars fly everywhere(interesting what will happen to them) and Light Flash of the God.

Or maybe it will make Flashes time to time, because of small asymmetry and imperfection of NS.
Or it may have 2 constant beams of Light, because of rotation of NS, and difference of potential energy on poles and some magnetic momentum.
Or it may look like DeadStar ship, and shoot beams from equator parts of that NS and eating poles.

IDK. But I would like to see that.

$\endgroup$
  • $\begingroup$ As baby BH have troubles to swallow atoms, you have to feed it one by one. What nonsense! An atom sized black hole could swallow more than one atom in a snap. An atom sized black hole would weigh more than a mountain. Its mass could pull in tons of material around it. $\endgroup$ – RichS May 21 '16 at 11:04
  • $\begingroup$ As example I took 9.46e-4 nm size BH, with Everest mass. It's 10^9 times bigger then OP stated. But it's significantly smaller then atom size Atom size called distance where they begin to interact with each other. Roughly speaking size of electron cloud around an atom. Yes atom size BH will swallow atoms easy, but still even in that case it will take long time. Roughly speaking speed depends how much atoms you may place around Schwarzschild radius.(at some point it will not matter, but for small it is) $\endgroup$ – MolbOrg May 21 '16 at 12:54
  • $\begingroup$ Yes, my answer is't correct in all aspects. Because it's focused on only one problem, which is derived from size. And insults only one believe, which states that BH is not only time-matter singularity, but singularity of anysort of everything which somehow connected with BH subject. BH is't like superman, it is an object with some properties, and most of them are finite. Feel free to investigate importance of BH size by your self, and post as new answer, I would like to read. $\endgroup$ – MolbOrg May 27 '16 at 13:04
  • 1
    $\begingroup$ A 600 KT black hole is insanely hot, 2E17 K -- this would push matter aware from the black hole due to radiation pressure (among other effects too). Another good reason to turn off Hawking radiation (an exercise left to the reader). $\endgroup$ – Gary Walker May 8 '18 at 3:26
1
$\begingroup$

How to create a 100 Earth mass black hole in 3 easy steps.

  1. Create 600K ton mass black hole.
  2. Drop tiny black hole onto 100 Earth-mass planet.
  3. Wait a few days while black hole consumes entire mass of planet.

All joking aside, this might be the easiest way to do it. If you made a tiny black hole and dropped it on Saturn, you would soon have a 95 Earth-mass black hole. A 600K ton black hole would be a very small black hole. To manipulate it, you just drop a bunch of electrons into it. It would accumulate the charge, and you can store it and move it around inside a magnetic containment field. It would be easier to manipulate than a much larger one - say one about the mass of Phobos.

$\endgroup$
  • $\begingroup$ you would soon have even if not to consider evaporation of that black hole, this soon will be hundreds of millions years. Because of speed limit 1c. Atom size black hole will grow ca 30 tonnes year, something like that, until the almost done it will be very very slow process. $\endgroup$ – MolbOrg May 19 '16 at 17:46
  • 1
    $\begingroup$ @MolbOrg Can you explain how the speed of light implies an atom sized black hole can't consume more than 30 tons per year? That's a very small amount of mass compared to the enormous mass of an atom size black hole. $\endgroup$ – RichS May 20 '16 at 5:41
  • $\begingroup$ I do remember reading something that suggested that a small black hole, on the order of a few 100 metric tons, has properties which have the effect of repelling the large majority of mass at a given radius, a couple of meters, but it may have been speculation. Worth looking into what actually happens regarding all possible forces involved. Seems magnetism and ionization were the primary factors at these scales. My apology for not providing a source, but it was many years ago and I'm sure the source was not scholarly, hence may have merely been curiosity and speculation by the writer. $\endgroup$ – Nolo May 20 '16 at 8:10
  • $\begingroup$ @Nolo you talking about black hole evaporation, that is well known theory Hawking radiation $\endgroup$ – MolbOrg May 20 '16 at 11:00
  • 1
    $\begingroup$ @RichS short speaking is because of finite size of atoms and because BH is way much smaller then interaction size of atoms. And yes as I recall now, after posting this answer, it was sort of 30t per million years, and not 30t per year. You may try to read that answer if you wish more details, how I came to that numbers-conclusion. $\endgroup$ – MolbOrg May 20 '16 at 16:25
1
$\begingroup$

According to Wolfram Alpha, the mass energy of $100$ earths appears to be $2.684\times 10^{43}\text{ Joules}$.

How quickly that amount of energy can be produced and what is required? A type 1A core collapse (supernova) produces $1.5\space \text{foe}$ ($\text{unit} =10^{44}\text{J})$, so it would be ~one order of magnitude smaller than the smallest type of supernova.

So as an approximation of timescale (minus an order of magnitude in energy level) - according to various answers on this physics.SO question, the implosion event happens in a few seconds (during which time all energy from the event is released from the core and partially absorbed by surrounding mass), but the illumination of external matter can last weeks.

Possible suggestion, feed your black hole to another black hole of 100 earth masses. My guess in that case is that the energies would be contained and not destroy everything within some (unknown) large radius... but then the question remains - where would you get that kind of black hole?

$\endgroup$
  • $\begingroup$ The other issue is that it will be impossible to focus all of the energy of the supernova on the right point. $\endgroup$ – HDE 226868 Mar 30 '16 at 2:03
  • 3
    $\begingroup$ Seems much easier to just feed the black hole mass directly rather than energetic massless particles like photons, especially since an exploding object like a supernova will never release more energy than was contained in the rest mass of the original exploding object. $\endgroup$ – Hypnosifl Mar 30 '16 at 2:46
  • $\begingroup$ @Hypnosifl Agreed, I did not think to make reference to the mass of the star that would collapse and produce such an event, however, the intention was simply to provide a context for comparison of the energies involved. $\endgroup$ – Nolo Mar 30 '16 at 3:26
  • 1
    $\begingroup$ @Nolo Possible suggestion, feed your black hole to another black hole of 100 earth masses. But if you already have a 100 Earth mass black hole, then you wouldn't need to create such a black hole in the first place. It's like saying "if you want to build a castle, then start with a single rock about the size of your hand and add it to a castle that already exists." See, you haven't really built a castle. Likewise, if you already have a 100 Earth-mass hole, you don't need to build one. $\endgroup$ – RichS May 20 '16 at 5:46
  • $\begingroup$ @RichS Agreed, I was merely exhausting other options regardless of their triviality, however, I was not clear and should have said "a black hole with 100 earth masses less the mass of the one you have to start with", but yes I see your point. Your answer does make more sense as far as starting with an 100 earth mass planet. $\endgroup$ – Nolo May 20 '16 at 7:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.