Black holes and only photons going in

[stanjones]

Build a Dyson sphere around a black hole (this is a thought experiment), so no more mass "falls in". Line the sphere with insanely bright lights. What happens to the black hole?

I ask this because Prof. Sean Carroll in "From Eternity To Here" discusses whether there is a limit to the entropy that can be put in a fixed space. He mentions using photons, but then drops that line of inquiry.

 

[tiny-tim]

welcome to pf!

hi stan! welcome to pf!

Build a Dyson sphere around a black hole (this is a thought experiment), so no more mass "falls in". Line the sphere with insanely bright lights. What happens to the black hole?

the photons (although they have no rest-mass) have energy and therefore mass, so the black hole gets more massive, and the Dyson sphere is now in the wrong position

 

[bcrowell]

Amplifying on what tiny-tim said, a black hole's radius is proportional to its mass-energy. As you add photons to it, its mass-energy increases, and so does its radius. Therefore you aren't using a fixed amount of space.

 

[stanjones]

Thank you both. I re-read the section in Carroll's book and it makes sense now, which for such a non-intuitive subject is something.

 

[mrspeedybob]

Sound like the most energy dense battery you could ever make. To charge it you turn on the lights and add photons/mass. To discharge you absorb hawking radiation and convert it to a usable form. Should work as long as you don't let the black hole completely evaporate.

 

[Nabeshin]

To discharge you absorb hawking radiation and convert it to a usable form. Should work as long as you don't let the black hole completely evaporate.

Unfortunately if you want to do this you have no control over the rate of energy extraction. Much better to use the penrose process, but that requires a rotating hole.

 

[mrspeedybob]

Unfortunately if you want to do this you have no control over the rate of energy extraction. Much better to use the penrose process, but that requires a rotating hole.

Sure you could control the rate of extraction...

Suppose your extraction method is thermal in nature. Hawking radiation heats the inside of the containment sphere. From there the heat either goes through a heat engine and performs work, gets radiated away from the black hole, or gets radiated back toward it where it falls back in. If you decide to run your heat engine at less then full capacity and your sphere is well insulated then most of the remaining energy from the hawking radiation will be coveted into heat and radiated right back into the hole.

 

[Nabeshin]

Sure you could control the rate of extraction...

Suppose your extraction method is thermal in nature. Hawking radiation heats the inside of the containment sphere. From there the heat either goes through a heat engine and performs work, gets radiated away from the black hole, or gets radiated back toward it where it falls back in. If you decide to run your heat engine at less then full capacity and your sphere is well insulated then most of the remaining energy from the hawking radiation will be coveted into heat and radiated right back into the hole.

But the black hole radiates at a fixed rate! So if your black hole is radiating 10J/s, you cannot extract more than 10J/s (as you point out, you can extract less, but not more). And since the radiation rate for any sizable black hole is paltry at best, you'll need to wait a very long time to get a sizable sum of energy.