Black Hole Engineering - Revision history

Lwcamp: /* Gravity Generation */

2026-08-01T23:05:13Z

Gravity Generation

← Older revision		Revision as of 15:05, 1 August 2026
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	g = G M / r<sup>2</sup>		g = G M / r<sup>2</sup>
	</div>		</div>
	where lower case g is the acceleration due to gravity, upper case G = 6.67430×10<sup>−11</sup> m<sup>3</sup>/kg/s<sup>2</sup> is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get ~~the same~~ gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.		where lower case g is the acceleration due to gravity, upper case G = 6.67430×10<sup>−11</sup> m<sup>3</sup>/kg/s<sup>2</sup> is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get more gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.

	Gravity on Earth has a value of g<sub>&oplus;</sub> = 9.8 m/s<sup>2</sup>. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g<sub>&oplus;</sub> at your feet your head will nearly be in freefall. So we also want the distance for 1 g<sub>&oplus;</sub> to be significantly larger than a human height.		Gravity on Earth has a value of g<sub>&oplus;</sub> = 9.8 m/s<sup>2</sup>. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g<sub>&oplus;</sub> at your feet your head will nearly be in freefall. So we also want the distance for 1 g<sub>&oplus;</sub> to be significantly larger than a human height.

Lwcamp: /* Rotating black holes */

2026-08-01T22:16:08Z

Rotating black holes

← Older revision		Revision as of 14:16, 1 August 2026
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	Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.		Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.

	A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is		A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.
	<div align=center> J = M<sup>2</sup> G / c = M<sup>2</sup> 2.22615×10<sup>-19</sup> m<sup>2</sup>/kg/s.</div> Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.
			Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is
			<div align=center> J = M<sup>2</sup> G / c = M<sup>2</sup> 2.22615×10<sup>-19</sup> m<sup>2</sup>/kg/s.</div>

	Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the <i>ergosphere</i>. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.		Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the <i>ergosphere</i>. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.

Lwcamp: /* Containment */

2026-04-19T03:44:16Z

Containment

← Older revision		Revision as of 19:44, 18 April 2026
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	But there is another issue to consider. If e &Vscr; / (T<sub>H</sub> k<sub>B</sub>), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) much larger than 1 and for T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) much larger than 1, the discharge rate is approximately e<sup>2</sup> &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) is about 10,000 and T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.		But there is another issue to consider. If e &Vscr; / (T<sub>H</sub> k<sub>B</sub>), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) much larger than 1 and for T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) much larger than 1, the discharge rate is approximately e<sup>2</sup> &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) is about 10,000 and T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

	But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 c<sub>s</sub>. The force on the black hole is v ṁ<sub>BH</sub>.		But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is v = √2 c<sub>s</sub>. The force on the black hole is v ṁ<sub>BH</sub>.

	Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10<sup>-11</sup> m/s<sup>2</sup>. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.		Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10<sup>-11</sup> m/s<sup>2</sup>. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

Lwcamp: /* Containment */

2026-04-18T16:18:10Z

Containment

← Older revision		Revision as of 08:18, 18 April 2026
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	For electric containment, it is interesting to note that because r<sub>S</sub></div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.		For electric containment, it is interesting to note that because r<sub>S</sub></div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.

	If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10<sup>-8</sup> kg m<sup>2</sup>/s. This gives it a magnetic dipole moment of m = 3.7×10<sup>-33</sup> A m<sup>2</sup>. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10<sup>-21</sup> N and an acceleration of about 3.7×10<sup>-32</sup> m/s<sup>2</sup>, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential.		If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10<sup>-8</sup> kg m<sup>2</sup>/s. This gives it a magnetic dipole moment of m = 3.7×10<sup>-33</sup> A m<sup>2</sup>. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10<sup>-21</sup> N and an acceleration of about 3.7×10<sup>-32</sup> m/s<sup>2</sup>, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential. In particular, for a given voltage and magnetic field gradient, the acceleration should scale linearly with the black hole mass, thus favoring larger black holes.

	But there is another issue to consider. If e &Vscr; / (T<sub>H</sub> k<sub>B</sub>), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) much larger than 1 and for T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) much larger than 1, the discharge rate is approximately e<sup>2</sup> &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) is about 10,000 and T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.		But there is another issue to consider. If e &Vscr; / (T<sub>H</sub> k<sub>B</sub>), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) much larger than 1 and for T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) much larger than 1, the discharge rate is approximately e<sup>2</sup> &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (T<sub>H</sub> k<sub>B</sub>) is about 10,000 and T<sub>H</sub> k<sub>B</sub> / (m<sub>e</sub> c<sup>2</sup>) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

Lwcamp: /* Containment */

2026-04-18T15:49:49Z

Containment

← Older revision		Revision as of 07:49, 18 April 2026
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	With modern accelerators, we might get electrons up to an energy of 1 TeV (1×10<sup>12</sup> eV), for a potential of &Vscr; = 1×10<sup>12</sup> V.		With modern accelerators, we might get electrons up to an energy of 1 TeV (1×10<sup>12</sup> eV), for a potential of &Vscr; = 1×10<sup>12</sup> V.
	For our example 100 million ton black hole, this gives a charge of Q = 1.65×10<sup>-14</sup> C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 10<sup>8</sup> V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10<sup>-17</sup> m/s<sup>2</sup>, or about 10<sup>-18</sup> g<sub>&oplus;</sub>. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.		For our example 100 million ton black hole, this gives a charge of Q = 1.65×10<sup>-14</sup> C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 10<sup>8</sup> V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10<sup>-17</sup> m/s<sup>2</sup>, or about 10<sup>-18</sup> g<sub>&oplus;</sub>. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.

			For electric containment, it is interesting to note that because r<sub>S</sub></div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.

	If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10<sup>-8</sup> kg m<sup>2</sup>/s. This gives it a magnetic dipole moment of m = 3.7×10<sup>-33</sup> A m<sup>2</sup>. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10<sup>-21</sup> N and an acceleration of about 3.7×10<sup>-32</sup> m/s<sup>2</sup>, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential.		If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10<sup>-8</sup> kg m<sup>2</sup>/s. This gives it a magnetic dipole moment of m = 3.7×10<sup>-33</sup> A m<sup>2</sup>. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10<sup>-21</sup> N and an acceleration of about 3.7×10<sup>-32</sup> m/s<sup>2</sup>, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential.

Lwcamp: /* Hawking radiation */

2026-04-13T14:19:59Z

Hawking radiation

← Older revision		Revision as of 06:19, 13 April 2026
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	<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 10<sup>9</sup> <td> >> 6 × 10<sup>9</sup> & << 1.2 × 10<sup>12</sup>		<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 10<sup>9</sup> <td> >> 6 × 10<sup>9</sup> & << 1.2 × 10<sup>12</sup>
	<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000		<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000
	<tr><td>Electromagnetic fraction <td> 90% <td> 17% <td> 7.6%		<tr><td>Electromagnetic fraction <td> 90% <td> 11.8% <td> 7.6%
	<tr><td>Gravitational fraction <td> 10% <td> 2% <td> 0.9%		<tr><td>Gravitational fraction <td> 10% <td> 1.4% <td> 0.9%
	<tr><td>Neutrino fraction <td> 0 <td> 81% <td> 55.7%		<tr><td>Neutrino fraction <td> 0 <td> 86.8% <td> 55.7%
	<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%		<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%
	</table>		</table>

Lwcamp at 18:59, 7 March 2026

2026-03-07T18:59:13Z

← Older revision		Revision as of 10:59, 7 March 2026
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	== References ==		== References ==

	[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]		[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]

Lwcamp: /* Containment */

2026-02-28T05:31:20Z

Containment

← Older revision		Revision as of 21:31, 27 February 2026
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	where ε<sub>0</sub> = 8.8541878188×10<sup>−12</sup> F/m is the vacuum permittivity.		where ε<sub>0</sub> = 8.8541878188×10<sup>−12</sup> F/m is the vacuum permittivity.
	The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is		The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C </div>
	and the energy to charge the black hole up is		and the energy to charge the black hole up is
	<div align=center> W = (1/2) C &Vscr;<sup>2</sup>.</div>		<div align=center> W = (1/2) C &Vscr;<sup>2</sup>.</div>

Lwcamp: /* Containment */

2026-02-28T05:30:23Z

Containment

← Older revision		Revision as of 21:30, 27 February 2026
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	You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.		You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.

	One problem is the electrical potential of the hole. ~~The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is~~		One problem is the electrical potential of the hole.
	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = (1/(4 π ε<sub>0</sub>)) Q / r<sub>S</sub></div>~~		A black hole will have a capacitance of
	~~where ε<sub>0</sub> = 8.8541878188×10<sup>−12</sup> F/m is the vacuum permittivity.~~ A black hole will have a capacitance of
	<div align=center> C = 4 π ε<sub>0</sub> r<sub>S</sub></div>		<div align=center> C = 4 π ε<sub>0</sub> r<sub>S</sub></div>
			where ε<sub>0</sub> = 8.8541878188×10<sup>−12</sup> F/m is the vacuum permittivity.
			The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
			<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C
	and the energy to charge the black hole up is		and the energy to charge the black hole up is
	<div align=center> W = (1/2) C &Vscr;<sup>2</sup>.</div>		<div align=center> W = (1/2) C &Vscr;<sup>2</sup>.</div>

Lwcamp: /* Containment */

2026-02-28T05:25:56Z

Containment

← Older revision		Revision as of 21:25, 27 February 2026
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	But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 c<sub>s</sub>. The force on the black hole is v ṁ<sub>BH</sub>.		But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 c<sub>s</sub>. The force on the black hole is v ṁ<sub>BH</sub>.

	Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10<sup>-11</sup> m/s<sup>2</sup>. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results.		Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10<sup>-11</sup> m/s<sup>2</sup>. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

	== Credit ==		== Credit ==