When a particle fall past the event horizon, is it possible to escape via quantum tunnelling?
Just my guess:
Since the particle is acclerating towards the center of the black hole, any quantum-tunneling potential would be expressed in that direction also.
well, from what I understand, quantum tunneling doesn't really have a "direction"
Er... yes it does. Look at the wavefunction. It has "k", the wave vector, which is built in into the tunneling matrix element. And directional tunneling is something that is used to study the density of states of material along a particular crystallographic direction.
I don't understand, how can it have a direction? It's not like when tunneling happens, a particle travels into any particular direction, it's just there. It doesn't traverse any space.
It has a direction depending on the orientation of the tunneling barrier and the direction of the particle's momentum, i.e. the "k" in the wavefunction. The largest probability of tunneling given a constant momentum magnitude is for the particle to be perpendicular to the barrier. So yes, there is a prefered direction.
Ok I kinda understand what you mean in that after a particle tunnels there is a particular direction in relation to where it was previously. But how does that prevent it from escaping a blackhole when direction is irrelevant?
I wouldn't know. I've never done tunneling through a blackhole barrier, and from what I can gather, neither have anyone else. Not only that, has anyone has actually established a theoretical description of such a thing? If not, aren't we just playing Let's Guess?
Well, granted that no one has made any direct observance, but I'm speaking about in theory. Does the laws of physics prevent this from happening?
You have established the formulation FIRST. There is a difference between our current understanding of tunneling, and what you are asking. Our conventional tunneling requires the existence of well defined space (and time) on both sides of the tunneling barrier, AND inside the tunneling barrier.
Do you have such a thing for your blackhole? How does one defined the "state" of a particle inside a blackhole? Is this a well-defined and well-developed physics?
I'm pretty sure i'm worng....but could hawking radiation be defined as a sort of tunneling?
No. It is the creation of particle-antiparticle pair near the event horizon where one gets swallowed, and the other doesn't.
does one of the particle-antiparticle pair have to tunnel out of the space near the event horizon in order to get out and get recorded as hawking raditation? because won't parts of the wavefunctionof the pair that will escape be kind of in the event horizon.
Er.. no. This occurs near and outside the event horizon. Why would it need to tunneling to be outside? It is already outside. But since the momentum of each particle will be opposite each other, it stands to reason that one of the pair will be moving towards the event horizon and gets swallowed, while the other can escape since it is already outside. Where is the tunneling barrier here?
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