Can Hawking Radiation explain the immortality of neutron stars?

[Dremmer]

If proton decay does not occur, are neutron stars immortal? I was hearing that that was the case.

 

[RocketSci5KN]

Well, I would think so. Clearly the neutrons are as stable as if they were in a nucleus, so the 'free neutron' half life (614 sec) doesn't apply. Some could decay into a proton and electron, but a large part of the star started out this way, and clearly neutrons are energetically preferred. I suppose it would just slowly cool off by radiating away photons until it matched the cosmic background temp...

Here's a question: Is the density of a neutron star higher at it's core than at the surface? Is there a theoretical limit to this density?

 

[twofish-quant]

Well, I would think so. Clearly the neutrons are as stable as if they were in a nucleus, so the 'free neutron' half life (614 sec) doesn't apply. Some could decay into a proton and electron, but a large part of the star started out this way, and clearly neutrons are energetically preferred. I suppose it would just slowly cool off by radiating away photons until it matched the cosmic background temp...

I don't think that neutron stars are immortal, because if there is proton decay then this will change neutron stars, but their lifetimes are much larger than the age of the universe.

Here's a question: Is the density of a neutron star higher at it's core than at the surface? Is there a theoretical limit to this density?

1) yes. You need higher density to support stuff

2) yes. If it gets too dense, then it collapses and turns into a black hole. What that theoretical limit is turns out to be very difficult to calculate since it involves dealing with a lot of nuclear physics that we don't really understand.

 

[bcrowell]

Over extremely long timescales, I would expect that neutron stars would either undergo collisions with other objects in their own galaxies, or else possibly be ejected from their galaxies.

 

[vanesch]

I don't know if there is something like "evaporation" of a neutron star, like there is evaporation of a black hole (assuming Hawking radiation to be true).

 

[twofish-quant]

I don't know if there is something like "evaporation" of a neutron star, like there is evaporation of a black hole (assuming Hawking radiation to be true).

Question: Does anything in Hawking's calculation require that the object producing radiation be a black hole? Does the Earth put out Hawking radiation?

 

[neilvanrijn]

I'd like to add two questions to this thread.
1. what is the relationship between a Bose-Einstein condensate and a neutron star
If you were able to produce a BEC of sufficient mass would that become a neutron star and or would a BEC produce something like Hawking radiation.

 

[Dremmer]

I don't think that neutron stars are immortal, because if there is proton decay then this will change neutron stars, but their lifetimes are much larger than the age of the universe.

I know that proton decay would make neutron stars mortal, but I was talking about if there isn't proton decay. If there isn't, are they immortal?

 

[Kracatoan]

Hawking radiation is nothing to do with whatever your mass is made out of, it is just the fact that when you haven a spontaneous creation of a particle-antiparticle pair, i.e electron and positron, one passes the black-hole's event horizon and the other one does not, this means the one which passes the event horizon is lost forever and the other one is emitted as radiation, of a sort. The Earth can't doo this because its gravity is too pitiful to prevent the pair joining back up and annihilating.

BECs and Neutron Stars arn't really that similar, in fact they are quite the opposite. A BEC is formed when the species within the compound no longer obey the Pauli Exclusion principle and effectively occupy the same space (but not really), whereas a neutron star only exists because the Pauli Exclusion principle is preventing the neutrons from collapsing in further.

Technically yes, if you had a BEC of sufficent mass it would form a neutron star, but this would only be because it would just be undergoing the same processes as a collapsing star:

Protons + Neutrons get crushed close together, pauli stops them getting too close, so they joina nd form neutrons => Neutron Star.

Which has nothing to do with the properties of BECs. The only similarity between a BEC and a neutron star is that they are interesting scientific objects.

 

[bcrowell]

Question: Does anything in Hawking's calculation require that the object producing radiation be a black hole? Does the Earth put out Hawking radiation?

You only get Hawking radiation if there's an event horizon. An event horizon is a defining characteristic of a black hole.

 

[twofish-quant]

You only get Hawking radiation if there's an event horizon. An event horizon is a defining characteristic of a black hole.

I need to go through Hawking's papers, but off the top of my head, I don't quite see quite why this is true. The event horizon is a global boundary, and when you cross an event horizon, there is nothing to tell you that you've crossed the event horizon.

The gravitational field of the Earth should be producing pairs of matter/anti-matter and if the anti-matter gets annihilated then you should see some radiation leakage through a Hawking like process.

For that matter a lot of the thermodynamic results that come from black hole seem to hold if you apply them to *any* boundary.

 

[bcrowell]

For that matter a lot of the thermodynamic results that come from black hole seem to hold if you apply them to *any* boundary.

It's certainly true that, e.g., an accelerated observer in Minkowski space will see Hawking radiation from a horizon that exists only because he/she is accelerating. But the energy source for this radiation is whatever energy source is accelerating the observer. I have never heard anyone suggest that, e.g., the Earth would evaporate on long time scales. I think that's just plain wrong; if you think it's correct, please provide some evidence. If you can get Hawking radiation observable from infinity in an asymptotically flat spacetime, from an object that has no event horizon according to an observer at asymptotic infinity, then I suppose proton decay would follow trivially from the existence of Hawking radiation??

 

[twofish-quant]

I have never heard anyone suggest that, e.g., the Earth would evaporate on long time scales.

Cool. That means I may have come up with something original. Time to pull up the research databases.

I think that's just plain wrong

Any particular reason or general gut feeling? The reason I'm asking is that if you have a specific reason in mind why it won't work (i.e. conservation of energy) they it may save me the trouble of spending a few weeks trying to get it to work.

if you think it's correct, please provide some evidence.

Right now, it's at the "gee this might be a cool idea" stage. To get it to a "I can publish in Ap J. Letters" is going to take another two or three months of work assuming that I don't spend a few weeks and then figure out that it won't work. Also, I'm not terribly possessive, if someone else wants to spend some time getting this into a journal article, feel free to steal the idea. I got lots of other stuff to do.

If you can get Hawking radiation observable from infinity in an asymptotically flat spacetime, from an object that has no event horizon according to an observer at asymptotic infinity, then I suppose proton decay would follow trivially from the existence of Hawking radiation??

Or electron decay. Suppose we establish that any massive object will produce Hawking radiation. What does that mean for an electron?

 

[bcrowell]

Or electron decay. Suppose we establish that any massive object will produce Hawking radiation. What does that mean for an electron?

The first thing I would worry about would be that there should be some time-scale for this decay of a particle of mass m. In units where c=G=1, there is only one time-scale that you can derive from m, and I think it comes out waaaaay wrong.

 

[Chronos]

Question - assuming Earth suddenly collapsed to form a black hole [reasons irrelevant], what would be its event horizon radius?

 

[bcrowell]

Question - assuming Earth suddenly collapsed to form a black hole [reasons irrelevant], what would be its event horizon radius?

2Gm/c^2

 

[Lievo]

Suppose we establish that any massive object will produce Hawking radiation.

Penrose would love it, wouldn't he? ;-)

 

[Chimps]

I need to go through Hawking's papers, but off the top of my head, I don't quite see quite why this is true. The event horizon is a global boundary, and when you cross an event horizon, there is nothing to tell you that you've crossed the event horizon.

The gravitational field of the Earth should be producing pairs of matter/anti-matter and if the anti-matter gets annihilated then you should see some radiation leakage through a Hawking like process.

For that matter a lot of the thermodynamic results that come from black hole seem to hold if you apply them to *any* boundary.

It's the event horizon which creates the effect.

You won't see it on anything without an event horizon because without it, the pairs will annihilate.

 

[TheTechNoir]

It's the event horizon which creates the effect.

You won't see it on anything without an event horizon because without it, the pairs will annihilate.

Right, that was my understanding too. The mass loss of the black hole is because of the SURVIVING half of the particle/anti-particle pair escaping the event horizon while the other is lost back to the black hole. Thus the larger a black hole the more slowly it evaporates. It doesn't make sense to me that virtual particle annihilation located on or around something would somehow make mass decrease and if that were the case the smaller an object was, such as my house the more rapidly it would evaporate.

It is virtual particles created right on the boundary of the event horizon and that is it I believe.

 

[Dremmer]

I remember once reading a while ago that neutron stars could in the distant future quantum tunnel into black holes? Is that actually the case, or just a myth?

 

[IsometricPion]

It doesn't make sense to me that virtual particle annihilation located on or around something would somehow make mass decrease and if that were the case the smaller an object was, such as my house the more rapidly it would evaporate.

The idea is that the curvature of space-time is what causes the virtual particles not to annihilate. If the tidal forces are sufficiently great, the virtual particles will be pulled apart and not be able to annihilate. The energy to create these new particles would come from the space-time curvature, and thus from whatever mass is producing it. It does not seem like an event horizon would be needed. The only limits on the radiation would be that the smaller the curvature the lower the energy (including rest mass) of the pairs produced.

However, it would probably be extremely difficult to measure Hawking radiation from anything other than a small black hole, since it is likely that less energy would be emitted due to this effect than is received from incident radiation (e.g., the Cosmic Microwave Background) (wikipedia indicates the mass would have to be less than that of the moon). So, while I think it is possible for a neutron star to evaporate via Hawking radiation it would take an incredibly long time (so other processes are probably a lot more important).

 

[bcrowell]

I remember once reading a while ago that neutron stars could in the distant future quantum tunnel into black holes? Is that actually the case, or just a myth?

It seems logical that such a process would be possible, but tunneling probabilities probably go something like $e^{-n}$, where n is the number of particles, so it seems unlikely to me that this would happen on any reasonable timescale compared the timescale for neutron stars to collide with other objects and form black holes that way. I'm also not sure that tunneling to or from a black-hole state can be handled without a full-fledged theory of quantum gravity, which we don't have. If you can track down a reference on this, that would be interesting to see.

 

[qraal]

I remember once reading a while ago that neutron stars could in the distant future quantum tunnel into black holes? Is that actually the case, or just a myth?

If protons are immortal, then neutron stars can tunnel. But for black-hole states to engulf an object composed of so many nucleons they'd require an immense amount of time. More likely the individual partons inside each nucleon will encounter black-hole states first and slowly tunnel away in a process that looks a lot like proton-decay. That happens in about 10^40-10^140 years.

 

[Chimps]

The idea is that the curvature of space-time is what causes the virtual particles not to annihilate. If the tidal forces are sufficiently great, the virtual particles will be pulled apart and not be able to annihilate. The energy to create these new particles would come from the space-time curvature, and thus from whatever mass is producing it. It does not seem like an event horizon would be needed. The only limits on the radiation would be that the smaller the curvature the lower the energy (including rest mass) of the pairs produced.

I think this is incorrect.

It is the unique nature of the event horizon which prevents otherwise certain annihilation.

 

[IsometricPion]

It is the unique nature of the event horizon which prevents otherwise certain annihilation.

The wikipedia pages on Hawking Radiation and the Unruh Effect together imply that an observer at infinity will observe a non-zero temperature for any object that produces acceleration. Since all gravitating objects cause the acceleration of all other objects, all gravitating objects should produce Hawking Radiation. As the Unruh article says, there is an event horizon produced by acceleration in Special Relativity called the Rindler horizon, this is a general result of acceleration, gravity is not required. (So, in a certain sense, we were both correct, an effective horizon is (probably) required, but a black hole is not.)