MadSci Network: Astronomy

Re: Does Hawking radiation include photons and gravitons?

Date: Thu May 3 14:20:12 2001
Posted By: Benjamin Monreal, Grad student, Physics, MIT
Area of science: Astronomy
ID: 988665659.As

Hey Stewart, good question!

First of all, I should point out that your description of Hawking radiation is not quite correct. Empty space full of virtual particle/antiparticle pairs; each pair has positive energy. This is a violation of the all-important Law of Conservation of Energy, so according to Heisenberg's Uncertainty Principle, the violation can only last for a short time t < 1/(E*2*pi*h), where h is Planck's constant. Now, either the particle or the antiparticle can fall into the black hole; if the other particle escapes, then the Heisenberg limit is violated - the particle has "stolen" a bit of energy from the vacuum, which gets replaced (in a manner I don't really understand) from the black hole. But it's incorrect to say that "the negative energy particle gets sucked in", and it's particularly incorrect to say "the antiparticle has negative energy". Either the particle or the antiparticle gets sucked in, and the other one escapes with positive energy.

Hawking radiation indeed can include all sorts of particles - both particles and antiparticles of all sorts, and photons. Photons can be produced in pairs; although a photon is its own antiparticle, they have to be produced in pairs with complimentary spins.

What type of particle-emission is most common? Well, Hawking radiation shows a "blackbody" spectrum - this means that the radiation emerging from the black hole will have some average or typical energy, which will be proportional to the black hole's "temperature". Hot objects have high-energy emissions, cool objects have low energy emissions. In the black hole's case, it turns out that large black holes are characteristically "cold" and small ones are "hot". Blackbody emissions also familiar on Earth, and they have the same emission-energy-to-temperature relationship. For example, an object at room temperature will emit radiation with a typical energy of 1/10 electron volt; this is enough energy to produce, say, an infared photon. Something as hot as the Sun will have a typical energy corresponding to an ultraviolet photon. An object at 2 billion degrees C would emit characteristic energies around 5 million electron volts - however, this is enough energy to create the mass of an electron-positron pair (E = mc^2). So, the typical emissions of an object at 2 billion degrees could include electrons (with 5 million eV of mass energy) as well as photons (gamma rays, with up to 5 million eV of kinetic energy)

Only something this hot is capable of emitting electrons and positrons. Only something 2,000 times hotter can emit protons and antiprotons. If you look at typical black holes - the smallest of which are thought to have 2 or 3 times the mass of the sun - you'll see that their temperatures are near absolute zero. The characteristic radiation of such a cold object is a very long, very low-energy radio-frequency photon! The emission of an actual massive particle or antiparticle is possible, but statistically very very rare. Only a very small black hole (unnaturally small in some respects) is hot enough to emit many massive particles!

So that's your answer; black holes, which tend to be very cold, tend to emit very-low-energy particles. The energy is not enough to manufacture anything as heavy as an electron, so it is mostly in the form of photons. At the end of a black hole's life, it eventually gets very small (and thus very hot) and only then emits all sorts of stuff in a runaway burst of energy.

As for gravitons, I have no idea. Right now, gravitons as particles are a purely theoretical idea. Not only are they unobserved, but the theories that predict them (like mSUGRA) are still way out in left field. I might venture a guess that gravitons (like neutrinos, but worse) are unimportant in Hawking radiation, since they are "weakly coupled" and thus do not like to engage in pair production.

An excellent reference (for both mathematical and non-mathematical descriptions) is at this link. You might also be interested to learn more about black bodies and the blackbody spectrum, for which a search of the MadSci site should help you.

Hope this helps,

-Ben Monreal

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