3 ms·

Gravitationally maybe, but you'd certainly notice the 9 kW of hawking radiation.

by IsTom 2y ago

simiones 2y ago
I believe black holes are not currently emitting any Hawking radiation, because the CMB is far too hot for now. They will start emitting Hawking radiation in the far future, after the Universe has cooled down significantly.
- IsTom 2y ago
  Hawking radiation depends on mass of the BH, the smaller the hole the hotter it is.
- sapiogram 2y ago
  No, the formula for the power of a black hole's Hawking Radiation is very straightforward, and it only depends on the black hole's mass.
  - ithkuil 2y ago
    I think the idea is that black holes can never shrink to a size small enough to emit a hawking radiation hotter than CMB as long as it receives photons from the CMB that that will balance the mass/energy of the black hole and keep it in equilibrium. This obviously is not a problem if you create a new very small black hole from scratch as it only applies to pre-existing black holes that are massive enough so that their hawking radiation temperature is lower than the CMB
- eigenspace 2y ago
  That's nice that you believe that, but your belief is wrong (for sufficiently small black holes)
- rachofsunshine 2y ago
  Black holes emit Hawking radiation regardless of ambient temperature. It's just that right now, the mass(-energy) of photons falling into the hole from the CMBR is outpacing the mass loss to Hawking radiation for large black holes, so large black holes aren't currently evaporating from their own Hawking radiation. It's like standing next to a campfire. Your body is still emitting thermal radiation in the IR, it's just that you're receiving more thermal radiation from the fire than you're putting out.
sapiogram 2y ago
What if it passed through you at hyperbolic velocity (with respect to earth)?
- ted_dunning 2y ago
  The assumption in the paper was 100km/s which is definitely hyperbolic. If you slow it down to solar escape velocity at the Earth (the borderline of what you might expect) you get 42km/s which is only a bit slower than in the paper. This would mostly have the effect of doubling your radiation exposure.
rao-v 2y ago
I thought this effect would dominate too, but it turns out the paper’s assumptions is that the PBH moves at 100 km/s so we’re talking about 5 joules while it’s inside you and maybe 1000 joules total while it’s in your vicinity. Hardly blood boiling stuff.
- rachofsunshine 2y ago
  It's important not to blow off a few joules when you're speaking of radiation. The LD50 dose for a 75 kg human is only about 375 J (5 Sv) of gamma rays[1]. In this case, the 5 J delivered inside you (I didn't check your calculations on this, just using your number), and perhaps another 5 on approach and exit, only end up being about 10 J (0.12 Sv), which is not enough to kill, but it is still a rather large radiation dose. It's more than twice the annual limit for occupational safety in the US, and is near the lower limit of the dose that could cause acute radiation syndrome. If the hole passed directly through your digestive tract, concentrating the dose in the vulnerable tissues there, there's a decent chance you'd get mildly sick. [1] Gamma rays have a weighting factor of 1 in the gray -> Sv calculation, and the black hole emits them isotropically, so they're roughly distributed across the body. So in this case, 1 Gy ~ 1 Sv.
  - queuebert 2y ago
    I agree. Absorbing 100 J (the paper's assumption) over an entire 75 kg body would be ~1.3 Gy whole-body dose, or 1.3 Sv for photons. That would probably make you sick. Traditional radiation therapy for cancer delivers 2 Gy/day x 30 days to the tumor to kill it. What if mysterious illnesses like fibromyalgia are just PBHs? Hmmm...
  - Etherlord87 2y ago
    > there's a decent chance you'd get mildly sick Aha! I finally know the cause!
    - PlunderBunny 2y ago
      Can you imagine trying to convince your insurance company? “No, it’s a very tiny black hole…”
ted_dunning 2y ago
Hmmm... I get 18kW for 1.4e17g Using Julia: > using Unitful > uconvert(u"W", Unitful.ħ * Unitful.c^6 / (15360 * π * Unitful.G^2) / (1.4e17u"g")^2) 18171.541554992324 W This is the same result as on https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator https://www.vttoth.com/CMS/physics-notes/311-hawking-radiati...
- IsTom 2y ago
  I got 9kW is for 2e17g and it's 35kW for 1e17g. I guess I didn't think about how quickly it grows.

Gravitationally maybe, but you'd certainly notice the 9 kW of hawking radiation.

by IsTom 2y ago

Gravitationally maybe, but you'd certainly notice the 9 kW of hawking radiation.

I believe black holes are not currently emitting any Hawking radiation, because the CMB is far too hot for now. They will start emitting Hawking radiation in the far future, after the Universe has cooled down significantly.

IsTom 2y ago
Hawking radiation depends on mass of the BH, the smaller the hole the hotter it is.
sapiogram 2y ago
No, the formula for the power of a black hole's Hawking Radiation is very straightforward, and it only depends on the black hole's mass.
- ithkuil 2y ago
  I think the idea is that black holes can never shrink to a size small enough to emit a hawking radiation hotter than CMB as long as it receives photons from the CMB that that will balance the mass/energy of the black hole and keep it in equilibrium. This obviously is not a problem if you create a new very small black hole from scratch as it only applies to pre-existing black holes that are massive enough so that their hawking radiation temperature is lower than the CMB
eigenspace 2y ago
That's nice that you believe that, but your belief is wrong (for sufficiently small black holes)
rachofsunshine 2y ago
Black holes emit Hawking radiation regardless of ambient temperature. It's just that right now, the mass(-energy) of photons falling into the hole from the CMBR is outpacing the mass loss to Hawking radiation for large black holes, so large black holes aren't currently evaporating from their own Hawking radiation. It's like standing next to a campfire. Your body is still emitting thermal radiation in the IR, it's just that you're receiving more thermal radiation from the fire than you're putting out.

sapiogram 2y ago

What if it passed through you at hyperbolic velocity (with respect to earth)?

ted_dunning 2y ago
The assumption in the paper was 100km/s which is definitely hyperbolic. If you slow it down to solar escape velocity at the Earth (the borderline of what you might expect) you get 42km/s which is only a bit slower than in the paper. This would mostly have the effect of doubling your radiation exposure.

rao-v 2y ago

I thought this effect would dominate too, but it turns out the paper’s assumptions is that the PBH moves at 100 km/s so we’re talking about 5 joules while it’s inside you and maybe 1000 joules total while it’s in your vicinity. Hardly blood boiling stuff.

rachofsunshine 2y ago
It's important not to blow off a few joules when you're speaking of radiation. The LD50 dose for a 75 kg human is only about 375 J (5 Sv) of gamma rays[1]. In this case, the 5 J delivered inside you (I didn't check your calculations on this, just using your number), and perhaps another 5 on approach and exit, only end up being about 10 J (0.12 Sv), which is not enough to kill, but it is still a rather large radiation dose. It's more than twice the annual limit for occupational safety in the US, and is near the lower limit of the dose that could cause acute radiation syndrome. If the hole passed directly through your digestive tract, concentrating the dose in the vulnerable tissues there, there's a decent chance you'd get mildly sick. [1] Gamma rays have a weighting factor of 1 in the gray -> Sv calculation, and the black hole emits them isotropically, so they're roughly distributed across the body. So in this case, 1 Gy ~ 1 Sv.
- queuebert 2y ago
  I agree. Absorbing 100 J (the paper's assumption) over an entire 75 kg body would be ~1.3 Gy whole-body dose, or 1.3 Sv for photons. That would probably make you sick. Traditional radiation therapy for cancer delivers 2 Gy/day x 30 days to the tumor to kill it. What if mysterious illnesses like fibromyalgia are just PBHs? Hmmm...
- Etherlord87 2y ago
  > there's a decent chance you'd get mildly sick Aha! I finally know the cause!
  - PlunderBunny 2y ago
    Can you imagine trying to convince your insurance company? “No, it’s a very tiny black hole…”

ted_dunning 2y ago

Hmmm... I get 18kW for 1.4e17g Using Julia: > using Unitful > uconvert(u"W", Unitful.ħ * Unitful.c^6 / (15360 * π * Unitful.G^2) / (1.4e17u"g")^2) 18171.541554992324 W This is the same result as on https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator https://www.vttoth.com/CMS/physics-notes/311-hawking-radiati...

IsTom 2y ago
I got 9kW is for 2e17g and it's 35kW for 1e17g. I guess I didn't think about how quickly it grows.