# Why don't baby black holes give off a lot of Hawking radiation and vanish before having the chance to grow?

Is it because they eat more than they eject? Or something else?

Edit ------- I mean black holes which have just started forming from stellar collapse. Should had mentioned this.

Edit 2 ----- When you have a ball of neutrons which is compressed to the maximum extent physically possible during stellar collapse, the spatial curvature would be maximum at the center and would decrease as we travel away from it. However even at this point nowhere is the curvature enough to prevent light escaping. Now somewhere between this point to the formation of singularity I suppose the 'light trapping' curvature would develop at the center and then expand outwards. So that should mean that the event horizon grows from zero to its final size in a non-zero amount of time. Even inside a black hole as far as I know the curvature decreases outwards. By this logic the Hawking radiation should start off as soon as the EH develops and should counter if not stop the growth of the black hole.

• @Edouard I mean when the star begins its collapse there should be a tiny BH first with a small event horizon which grows as more stellar matter falls in. Aug 24 '20 at 15:00
• I think that's standard with stellar black holes generally--the horizon of the BH propagates outward from the center of the collapsing star--but, since I've only seen the adjective "baby" applied to black holes in connection with the creations of "baby" LU's (local universes, or regions causally-separated from all regions exterior to them)--I'd been wondering whether you'd looked at the cosmologies (at least including Poplawski's, as well as Smolin's older "cosmological natural selection") that are described as creating "baby universes". You might try adding a "cosmology" tag, for details. Aug 24 '20 at 18:13
• IIRC, in toy models of black hole formation, e.g., infalling dust, the black hole forms instantaneously once the density reaches a critical level. It does not start out small and expand. I suspect that the same may be true when a black hole is formed in a stellar collapse. Aug 24 '20 at 23:21
• Related: physics.stackexchange.com/a/188864/123208 & physics.stackexchange.com/a/273328/123208 where Rob Jeffries explains that "the addition of more and more momentum to the particles in order to provide the required higher and higher central pressures is ultimately counterproductive, because in GR this additional pressure and momentum simply add to the gravitational field that is crushing the star inwards." Aug 25 '20 at 12:59
• Midovaar, looking at your latest edit, you seem to be assuming that the event horizon forms when the curvature reaches a certain critical level. My knowledge of the subject is cursory and several decades old, but I believe this assumption to be false. Sorry, I know that "it's more complicated than that" is an unsatisfactory response! If you don't get an expert answer here, you might try Astronomy? Aug 25 '20 at 22:14

There are lots of "black hole lifespan calculators" on the internet. This one by Viktor T. Toth seems to be particular comprehensive. A black hole with the same mass as our sun would take at least $$2 \times 10^{67}$$ years to evaporate due to Hawking radiation. This lifetime goes up with the cube of the black hole's mass. And we expect black holes that form from stellar collapse to be at least as massive as our sun, and probably several times as massive. As Toth says:

The lifetime of a one solar mass black hole, therefore, is calculated as more than 57 orders of magnitude longer than the present age of the universe. But that does not take into account the fact that such a black hole is colder than the cosmic microwave background radiation bathing it. Therefore, whatever little energy it radiates, it actually receives more in the form of heat from the cosmos. So rather than shrinking, it would continue to grow. Indeed, any black hole with a mass greater than about 0.75% of the Earth's mass is colder than the cosmic background, and thus its mass increases for now. As the universe expands and cools, however, eventually the black hole may begin to lose mass-energy through Hawking radiation.

• I think the question is not about black holes that have already reached stellar mass. Rather, during stellar collapse, there is a transition from "no black hole" to "part of the core is a black hole," and presumably during that transition there is a point where the mass within the event horizon is very small.
– rob
Aug 24 '20 at 15:59
• @gandalf61 : What I mean is that when stellar collapse happens wouldn't there be a tiny black hole first with a small event horizon which would grow as more matter around it fell into the singularity? Or does the event horizon form instantly instead of starting from a minuscule diameter? Aug 24 '20 at 16:01
• @rob Thanks for understanding my admittedly poorly structured question. Aug 24 '20 at 16:03
• Since 2014, as per the link at scientificamerican.com/article/… , "apparent horizon" is the description of the collapsing or collapsed star's outward-propagating horizon that's preferred in verbal descriptions of the collapsed or collapsing star's volume by well-informed adherents of Hawking radiation propagating outward, whereas "event horizon" is used by others, and by persons unaware of that subtle change in Hawking's terminology. HR was mathematically formulated in 1974: His change was forced by argument. Aug 24 '20 at 18:43
• A cosmology whose theoretical & physical observations may've factored into the change in Hawking's terminology is described at arxiv.org/pdf/1305.6977.pdf : As can be seen in the last section of that 2013 paper, it posits the Hawking radiation as propagating inward, from each of the local universes whose shape its author has described elsewhere as "a three-dimensional analog of the surface of a...ball". Aug 24 '20 at 19:17

I would add to gandalf61's answer, that Hawking radiation is seen from the point of view of an exterior observer, but an exterior observer does not see a black hole form from a collapsing star. He sees a "frozen star" in which time "stops" and the event horizon does not form until the infinite future.