# Hawking Radiation seems contrary to black hole dynamics

• jaketodd
So, yes, negative and positive energy particles are equally likely to fall into the hole. The negative energy particles, however, do not negate the positive energy particles. The negative energy particles are negative energy with respect to an observer at infinity. To an observer at the event horizon, the negative energy particles are negative spatial momentum. Since positive spatial momentum is necessary for a particle to escape from the black hole, the negative energy particles cannot escape. They are still negative energy, but they are negative energy that is moving in the wrong direction with respect to spatial momentum. Therefore, they cannot contribute to Hawking radiation. Only positive energy particles can contribute to Hawking radiation, and they are positive energy with respect to both an outside observer and an observer at

#### jaketodd

Gold Member
My understanding of Hawking Radiation is that a particle and anti-particle form at the event horizon, the particle escapes, the anti-particle goes into the black hole, annihilates a particle at the core of the black hole, and energy is released, leading to an evaporating black hole. But how do the particles that are the result of annihilation get out of the event horizon if not even photons can escape?

Thanks,

Jake

Nothing gets out of the black hole. The vacuum fluctuation occurs just outside the event horizon. One particle escapes, and the other enters the black hole. The anti-particle negates whatever is in the hole, forming nothing, as in 1+(-1)= zero.
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Of course I may be wrong, as it seems to me that particles and anti-particles would have an equal chance of entering the hole, thus negating each other instead of anything in the hole. What am I missing?

It is my understanding that annihilation isn't really annihilation; new particles are formed obeying the conservation of energy. ??

Algr said:
Nothing gets out of the black hole. The vacuum fluctuation occurs just outside the event horizon. One particle escapes, and the other enters the black hole. The anti-particle negates whatever is in the hole, forming nothing, as in 1+(-1)= zero.
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Of course I may be wrong, as it seems to me that particles and anti-particles would have an equal chance of entering the hole, thus negating each other instead of anything in the hole. What am I missing?

This comes up often; see
George Jones said:
When virtual matter-antimatter pairs are created, the probability that the antimatter particle has positive energy is equal to the probability that the matter particle has positive energy, i.e., both probalilities are 1/2.

Hawking radiation does not come about because antimatter particles sometimes fall into black holes; it comes about because negative-energy particles (both matter and animatter) sometimes fall into black holes. Some popular-level treatments of black holes obscure this, and even sometime get this completely wrong.

Sometimes it is difficult to give accurate non-mathematical descriptions of processes that involve advanced physics. This is particularly true for Hawking radiation - it is very hard to see the correspondence between the non-mathematical description involving virtual matter-animatter pairs and the actual mathematical description.

Steve Carlip is a physicist who tries hard to make physical concepts clear, both for laypersons and for experts. You should read his non-mathematical description of Hawking radiation, which is more challenging than most non-mathematical descriptions, but which also is more accurate than most non-mathematical descriptions. If you have questions about his description, just post them.

What happens, very roughly, is this. Energy is associated with time and spatial momentum is associated with space. When an matter-antimatter pair of virtual particles is created *outside* the event horizon, they can become a little bit separated in the time that the Heisenberg uncertainty principle allows them to live. Tidal forces caused by the curvature of spacetime help them to separate, and, sometimes, the negative-energy particle (which could be either matter or anitimatter) wanders over the event horizon and into the black hole. Inside the event horizon, the roles of time and space coordinates get interchanged. Thus, according to what I wrote above, the roles of energy and spatial momentum get interchanged. What was negative energy becomes a negative spatial component of a local (for an observer inside the horizon) momentum vector. Only a virtual particle can have negative energy, while any particle, real or virtual, can have a negative component of spatial momentum.

Bottom line: the whole process can become a real process. In this real process, an observer outside a black hole "sees" the black hole hole swallow a negative-energy particle while emiitting a positve energy particle (the other member of the matter-antmatter pair). The balck hole radiates.

Regards,
George

So I should have said " negative energy particle" instead of anti-particle. But that doesn't change the basic question - aren't negative and positive energy particles equally likely to fall into the event horizon? Wouldn't they just cancel each other out?

Algr said:
So I should have said " negative energy particle" instead of anti-particle. But that doesn't change the basic question - aren't negative and positive energy particles equally likely to fall into the event horizon? Wouldn't they just cancel each other out?

From the link that I gave,
Steve Carlip said:
Note that this doesn't work in the other direction -- you can't have the positive-energy particle cross the horizon and leaves the negative- energy particle stranded outside, since a negative-energy particle can't continue to exist outside the horizon for a time longer than h/E. So the black hole can lose energy to vacuum fluctuations, but it can't gain energy.