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The pdf at arxiv.org/abs/hep-ph/0104160 is about the electroweak plasma surrounding a small black hole of around 700 kg mass.

A radiated electron passing through the electroweak layer surrounding the event horizon will be massless in this layer and presumably travels at the speed of light. When it moves outside the electroweak layer the electron will slow down as it gains mass from the Higgs field. Such an electron will have a slightly higher speed at a long distance from the black hole than Hawking's theory would predict.

Have I reasoned this out correctly?

jng224
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    FWIW, a Schwarzschild BH of 700 kg has a radius of $r_s=1.03962×10^{-24}$ m, a temperature of $1.75279×10^{20}$ K, and a lifetime of just under 29 ns. From https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator – PM 2Ring Mar 11 '21 at 21:21
  • The conclusion might be correct (I don't know), but I would challenge the reasoning: what is "an electron" in the phase where the electroweak symmetry is unbroken? The relationship between particles before and after electroweak symmetry breaking involves more than just the acquisition of mass, but I don't understand that relationship well enough to write a good answer. – Chiral Anomaly Mar 12 '21 at 01:46

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The electroweak layer described in that paper is actually caused by the Hawking radiation. See under figure 1:

A black hole with a mass 76 kg ∼ 200 tons can heat up its neighborhood by the Hawking radiation and restores the electroweak symmetry in the neighborhood spherically.

The electroweak fields have two basic states: a low-temperature state in which the Higgs field has a nonzero energy density (condensate) everywhere, and everything except the photon has a mass because of interactions with the condensate; and a high-temperature state in which the condensate has dissolved, there's a plasma of electroweak particles, and they are all massless.

The temperature needed to create an electroweak plasma is so high that (according to the standard understanding of astrophysics) it has existed almost nowhere in the universe since the big bang. But since the temperature of Hawking radiation increases as a black hole shrinks, near the end of its life, the radiation from an evaporating black hole would eventually cross that threshold. The Hawking particles would just be pouring out, and should create a zone around the black hole in which the Higgs condensate can't exist. It's vaguely similar to the flame around a burning candle. Outside that electroweak "flame", physics is back to normal, the Higgs condensate exists, and the Higgs mechanism is at work. Again, see figure 1 in the paper. (The "domain wall" is a transitional shell between the two states of the Higgs field.)

As for your deduction, well, it's true that if a black hole surrounded by electroweak plasma emitted an electron that started massless and moved in a straight line through the plasma into the empty space beyond, then it would indeed get there a fraction more quickly than if it had its usual mass all the way. But that's not a violation of the Hawking theory of black hole evaporation, it just shows that the second scenario is an oversimplification, for a small enough black hole.

Mitchell Porter
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