Does this account for the emission of gravity waves as well? IIRC you have Hawking Radiation and gravity waves taking energy away from the black hole. Is the background radiation sufficient to overcome that and keep the hole growing for the next hundred billion years or so?
T[sub]BH[/sub] = hc[sup]3[/sup]/4GkM[sub]BH[/sub] =>
M[sub]BH[/sub] = hc[sup]3[/sup]/4GkT[sub]BH[/sub]
using the CMBR (2.9K) as T[sub]BH[/sub] that leads to:
M[sub]BH[/sub] = 1.67e24 kg
which is less than a millioth of a solar mass.
as:
R[sub]BH[/sub] = 2GM[sub]BH[/sub]/c[sup]3[/sup] =>
R[sub]BH[/sub] = 0.0012 m
The basic meaning of the equations above is that for a black hole to be emitting more Hawking radiation than taking in CMBR it would have to be less than a millionth of a solar mass and have a Scwarzchild radius of about 1 millimetre, which is much, much smaller than could occur by stellar collapse. Though as the CMBR cools a black hole that is not accreting matter will begin to slowly evapourate.
MC Master of Ceremonies:
Does emitting gravity waves have any noticeable effect? I know gravity is by far the weakest of the fundamental forces but as a black hole shows get enough gravity together in one place and its effects can be stunning. IIRC Stephen Hawking said the earth emits enough energy in the form of gravity waves (kinda like a cork bobbing in water) to run an electric toaster (which is admittedly quite small). Still, why your Hawking Radiation decreases* with the size of the black hole wouldn’t emission of gravity waves increase?
*- Does Hawking Radiation decrease when a black hole gets larger or is it just more spread out so it is seemingly weaker? That is, is the emission of Hawking Radiation a constant for all balck holes (if you could capture ALL of the radiation it emitted)? I ask because it would seem the surface area of the event horizon would allow for the capture of correspondingly more virtual particle pairs but it obviously doesn’t happen that way. Further, I wonder if you added up ALL energy emissions from a black hole (gravity and Hawking radiation) if you would see a constant effect…as one goes up the other goes down).
Oops stupid algebra mistake!
First and second equations should be:
T[sub]BH[/sub] = hc[sup]3[/sup]/16pi[sup]2[/sup]GkM[sub]BH[/sub]
and
M[sub]BH[/sub] = hc[sup]3[/sup]/16pi[sup]2[/sup]GkM[sup]BH[/sub]
which means:
M[sub]BH[/sub] = 4.23e22
which is just over a 50 millionth of a solar mass, and
R[sub]BH[/sub] = 0.000030 m
or 0.03 mm
I’ve also read that the entire universe can be considered to be a black hole. I’m not sure how that can be, but if so, look around, you’re in one.
Oops stupid algebra mistake!
First and second equations should be:
T[sub]BH[/sub] = hc[sup]3[/sup]/16pi[sup]2[/sup]GkM[sub]BH[/sub]
and
M[sub]BH[/sub] = hc[sup]3[/sup]/16pi[sup]2[/sup]GkM[sup]BH[/sub]
which means:
M[sub]BH[/sub] = 4.23e22
which is just over a 50 millionth of a solar mass, and
R[sub]BH[/sub] = 0.000030 m
or 0.03 mm
.
A non-accelrating Schwarzchild balck hole won’t produce gravity waves, just like a stionery chrage doesn’tt emit em waves. Your going to have to ask Chronos for exactly how the mass of a black hole would decrease if it was emitting gravity waves.
The evapouration of a BH is proporional to the cube of it’s mass, i.e. a smaller black hole is losing mass alot quicker than a larger black hole.
I never get this part. Isn’t everything in the Universe technically moving? A black hole in a galaxy will be orbiting galactic center like any other star. A black hole in the center of the galaxy is moving with the galaxy itself (which I suppose might be said to orbit some common point but I don’t know for certain). Is it being suggested that a black hole can be found and said to be an object that is motionless by which all other motion can be referenced? I thought that was impossible? Given that shouldn’t every black hole everywhere be considered to emit gravity waves?
Yyour right your realistically not going to find a black hole without angular momentum of some sort, but a black hole that’s not acclerating can’t be taken as an absolute refence point as it will have different velocities in different reference frames none of which are prefered.
I realize we’re getting off topic here but since I think the OP has been answered and we’re on about it anyway I hope it’s ok.
I know reference frames can be difficult creatures to get a handle on. Just when I think I’ve got the sense of it some weirdness makes me wonder if I ever did at all. So…
Say we have a black hole (stellar mass) and a guy in a spaceship approaching each other at 0.25c. For the sake of argumetn there is nothing else in the universe…just these two objects. As I understand it reference frames dictate that it is impossible to say which one is moving. It is correct to say that the black hole isn’t moving but the spaceship is and at the same time the reverse is equally correct or any combination of velocities that add up to your 0.25c figure. It is correct to say all of those possibilities are correct answers at the same time.
However, can we use gravity waves as an indication of who is really moving here? I assume the more motion you have in the black hole the more gravity waves you’ll get (the spaceship is likewise emitting gravity waves but I think we’ll have a better chance of sensing this from teh stellar mass black hole). As such could our spaceman take a measurement of gravity waves emanating from the black hole (assuming he had such a device) and then calculate the velocity necessary for a black hole to generate that field? If the black hole is motionless (per what you said) it should emit zero gravity waves so I assume if that were the case the spaceman would get no measurement and he could say he alone is moving at 0.25c. If the black hole is moving then you’ll start getting gravity emissions.
I suspect I’m missing something here.
A black hole in uniform motion (i.e. constant velocity) doesn’t emit gravity waves, so from the spaceman’s point of rest-frame it would be the black hole not him whose travelling at a uniform 0.25c. In special relativty accelartion is not relative, it’s absolute, in general relativity it’s relative but you have to factor in the curvature of space-time.
A black hole will emit very violent gravitational waves, for a very short period of time when it initially forms. For a stellar-mass hole, this time will only be of the order of microseconds. Then, it settles down, and doesn’t emit any more.
If a black hole is orbiting some other object, then, like any pair of objects orbiting each other, the system will emit gravitational waves. You can’t really say that they’re coming from the black hole, though: They’re coming from the whole system. Only the orbital energy is available to be turned into gravitational waves; you can’t decrease the mass of the hole itself in this manner. Black holes do have one advantage in the production of gravitational waves: The strength of the waves will depend on how close the orbiting objects are to each other, and you can get closer to a black hole than you can to any other object of the same mass. Eventually, two black holes orbiting each other would lose so much orbital energy that they merge, producing a very distinct chirp in the gravitational wave signal. Once we get space-based detectors launched, we expect to hear a lot of these chirps.
Hawking radiation does depend on the size of the black hole. The effective temperature of the radiation is proportional to the surface gravity, and the surface gravity is inversely proportional to the size of the hole. Total luminosity of a hot blackbody (and a black hole is, unsurprisingly, an excellent blackbody) is proportional to the surface area times the fourth power of the temperature. So the total Hawking luminosity of a black hole is inversely proportional to the mass squared. If it helps your understanding, a large black hole has less Hawking radiation for the same reason that you can survive falling into a black hole: The tidal effects are smaller for a large black hole, and it’s effectively tidal forces which pull apart the virtual particles of Hawking radiation.
Quite right, Chronos. My information about black holes comes from a comic book (specifically, an early issue of Nexus). I’ll shut up now and defer to the people who actually majored in Astronomy and Physics.
You mean Nexus isn’t the bible on Astronomy? Crap…:smack: