Ask Science @lemmy.world niktemadur @lemmy.world 7d ago

How long would it take for a supermassive black hole like Sag A* to emit a tablespoon of mass via Hawking Radiation?

In the same vein, what about a stellar-sized black hole like Cygnus X-1? At this size the rate of evaporation is quicker, right?

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I've not got figures to hand, but it's incredibly slow. They are effectively perfect black body radiators, with their apparent temperature linked to their mass. The bigger they are, the colder they are.

Some back of the envelope calculations.

Right now, they are considerably colder than the cosmic background radiation, and so losses to hawking radiation are overwhelmed by even this. I just did a quick calculation on the milk way supermassive black hole, and it's about 1.5x10^-16 °C. That would work out as around 3x10^-91W/m2 or around 1x10^-71W. It's about 1x10^13 Joules per gram of matter. So you're looking at 10^84 seconds. The universe is about 4.4x10^16 seconds old, so around 10^68 times the current age of the universe.

To emit 1g will take around 100000000000000000000000000000000000000000000000000000000000000000000 x the age of the current universe. This ignores infalling energy.
- On Lemmy, superscripts need to be surrounded by carets.
  
  For example, this:
  
  3x10^-91W/m^2
  
  Needs to be this:
  
  3x10^-91^W/m^2^
  
  3x10^-91W/m2
  
  Vs.
  
  3x10^-91W/m²
  
  (If any app displays these incorrect superscripts correctly, then that app is doing it wrong. Last I knew Sync for Lemmy was wrong, but I stopped using it months ago for reasons such as this.)
  
  Screenshot from the website showing how it currently looks:
- It seems like a ridiculously huge amount of time for such a small amount, more so considering that according to theory these black holes will eventually evaporate completely.
  
  But then I try and visualize just how much it actually takes to go from 10^99 to hit the 10^100 (googol) milestone, and it's just too big a numerical chasm to truly wrap one's mind around. It all reaches the level of bizarre abstractions way, way, waaaay before that point.
  
  Something I like to think about is when we die, assuming there's no afterlife, then you don't feel the passage of time. A second or trillion of years is the same. If there's ever a point in that future where you'd gain consciousness again somehow, then you'd feel as if you'd be there the second after you died. It doesn't really relate to black holes but I felt like sharing the thought anyway.
  
  That evaporation rate is so small that you can think of black holes as eternal. However, it’s still not zero, so in extremely long time scales, it begins to make a deference. That’s when the heat death of the universe comes in, but those time scales are just ridiculous.
A tablespoon is a measure of volume, not mass
- Ack, ya got me! My mistake.
  One tablespoon of sugar is NOT equal to one tablespoon of neutron degenerate matter, that's for freaking certain.
  I was thinking more along the lines of something like sugar.
- I think it's fine to say a tablespoon in this case. You use tablespoon when you're not being exact, it just means "a small amount". Science communication needs to know when to be literal and exact (as in when you design safety measures for radiation, e.g.) and when you can just talk like a normal human being that doesn't have a stick up their degree.
  
  It's kind of interesting to note that you can't have "a tablespoon of blackhole", since they don't have a volume. But you shouldn't let that stop you from answering the question.
- It works well enough here. It's bigger than a microgram, and smaller than a kilogram. With the numbers we are working with, being within several orders of magnitude would be an impressive answer.

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