Does Hawking Radiation preclude EH formation?

[stevendaryl]

If we follow the worldline of a neutron that remains at rest at r = 0, that neutron sees a gradually increasing density and pressure, but at the instant the horizon forms, the density and pressure it sees is still finite; it is not until some time later on that neutron's worldline that a singularity of infinite density and pressure forms (when the surface of the neutron star collapses to r = 0).

I'm a little confused by the phrase "at the instant the horizon forms". If the neutron is at the center, and the horizon is at a nonzero radius, then you need a notion of simultaneity to say "at the same instant". What notion is appropriate here?

 

[Dale]

the center of a neutron star on the verge of gravitational collapse is <understatement>not that close to vacuum</understatement>.

excellent post!

 

[PAllen]

Even though it is not realistic, to get at the fundamental problem with treating BH formation as growth from a initially microscopic BH - which is simply wrong, always - think about a collapsing shell of matter.

When the event horizon forms in the center, the shell is still just outside the SC radius, and there is no mass at all inside the horizon. The horizon grows and shell shrinks until they meet at the SC radius. That's when the apparent horizon appears all at once, matching the event horizon. At this point, there is still no singularity and the matter density at the center is still zero. Some time later, the shell reaches the center, density goes infinite, singularity forms.

More realistically, consider an idealized collapse of a trillion star cluster - O-S collapse with stars as 'effective dust'. You have the absolute and apparent horizon encompassing the entire cluster while the stars all through cluster - including the center - still e.g. a billion miles apart. BH formation is intrinsically a global process in GR.

Now, what I can't answer (it is outside my expertise) is exactly when, in the above processes, Hawking or pre-Hawking radiation would begin. However, the inescapable conclusion is that applying simple formulas for 'old stable BH' to the formation process does not work at all.

 

[PeterDonis]

I'm a little confused by the phrase "at the instant the horizon forms". If the neutron is at the center, and the horizon is at a nonzero radius, then you need a notion of simultaneity to say "at the same instant". What notion is appropriate here?

At the instant the horizon forms, it has zero radius; it forms at r = 0 and spreads outward at the speed of light. So the "instant" I mean is the instant of the neutron's proper time when the horizon forms at r = 0.

 

[PeterDonis]

what I can't answer (it is outside my expertise) is exactly when, in the above processes, Hawking or pre-Hawking radiation would begin.

AFAIK nobody has seriously considered that question; but I'm not intimately familiar with the entire literature on this topic. Off the top of my head, I would say that Hawking radiation requires a locally trapped surface, i.e., an apparent horizon, and a trapped surface doesn't form until the collapsing object is entirely within r = 2M. But I haven't seen any math addressing this.

 

[PAllen]

AFAIK nobody has seriously considered that question; but I'm not intimately familiar with the entire literature on this topic. Off the top of my head, I would say that Hawking radiation requires a locally trapped surface, i.e., an apparent horizon, and a trapped surface doesn't form until the collapsing object is entirely within r = 2M. But I haven't seen any math addressing this.

That was my intuition as well, but I didn't want to state it without some backing (either from literature or understanding well enough how to apply the derivation(s) of Hawking radiation to the given scenarios). If this intuition is right, it still says Hawking radiation begins not only when all matter is at finite density, but even when there might no matter at all near 'where the singlularity will be'.

 

[atyy]

The Visser review references Nielsen's paper which discusses "Perhaps strongest reason for focusing on event horizons instead of apparent horizons was the belief that if an apparent horizon exists then it must lie behind the event horizon and so cannot influence the outside region anyway. As we will now see, this belief was predicated on a condition that is most probably violated by Hawking radiation. ...If one allows the possibility that a black hole spacetime will eventually stop accreting matter and start evaporating by the Hawking process, once must face the possibility that locally defined horizons, based on marginal surfaces, maybe located outside the event horizon, at least for some period of the lifetime of the black hole. In fact, the violation of the null energy condition opens up the further possibility that there is no event horizon at all and all one need consider is the trapping horizon"