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September 29

Must a given body, that has just been a black hole, always remain a black hole, as long as the body exists?

In other words, what rules out the following scenario?

1. A body, being right now a Schwarzschild black hole, starts emitting Hawking radiation.

2. However, the body's radius remains constant during the emission.

3. When the body has lost too much energy - along with its equivalent mass, the body's mass inside the constant body's radius becomes less dense, untill the body's current radius becomes bigger than the body's Schwarzschild radius - because of the stability (constancy) of the body's radius, so the body - which has just been a black hole - stops being a black hole and becomes a regular body.

What's wrong with this scenario? Is this really assumption #2 ? HOTmag (talk) 18:54, 29 September 2024 (UTC)[reply]

THe theory says #2 is wrong - black holes become smaller as their mass goes down. NadVolum (talk) 19:10, 29 September 2024 (UTC)[reply]

Yes, both our article black hole and our article Hawking radiation state that when the black holes emit radiation they "shrink", but how do you know that their shrinkage refers, not only to the body's mass, but also to the body's radius? This is the main question of this thread.

Is this because of the internal gravitation, which is the only "force" active inside the black hole? HOTmag (talk) 19:47, 29 September 2024 (UTC)[reply]

I think you're giving the word 'body' too much meaning. The radius is a gravitational result which depends on the mass.You wouldn't notice the surface as you fell through. NadVolum (talk) 20:33, 29 September 2024 (UTC)[reply]

I used the term "body" on purpose. A given body, whether a black hole or a billiard ball, has a radius, literally speaking. It's a fact you can't ignore. Nor can you ignore the influence of the body's radius on the density of the body's mass, hence on the question of whether this body is a black hole, because the body's radius is not necessarily identical to the body's Schwarzschild radius: Actually the former is not bigger than the latter if and only if the body is a black hole. This is the basis of my #3 assumption. If you don't agree to it, please explain what's wrong there, in your opinion. If you do agree to it, then I'm still asking the question in my previous response. HOTmag (talk) 09:10, 1 October 2024 (UTC)[reply]

Assumption #4: a hole is not a body. 176.0.159.38 (talk) 10:04, 1 October 2024 (UTC)[reply]

Our article black hole refers to "the nearest known body thought to be a black hole, Gaia BH1". It also refers to Cygnus X-1 as the first "object" identified as a black hole. Actually when I wrote "body" I meant a region, located in spacetime, and characterized by dense mass which doesn't let light escape when it's close enough. What's wrong in that view? HOTmag (talk) 11:41, 1 October 2024 (UTC)[reply]

Do you think an atom is a body? What use is the concept of density for an atom, where is that density? Density has even less real meaning for a black hole than it does for an atom, you can calculate a number by dividing one number by another but what then - what does it actually refer to? NadVolum (talk) 12:39, 1 October 2024 (UTC)[reply]

Is a stellar black hole a body? Let's check out: Does it have a mass? If it does, then does this mass have a location? If it does, then is this mass located in one geometric point? If it doesn't, then the mass must be located in some region. Does this region have an (average) radius? If it does, then we can sum up: a stellar black hole has a mass located in an (average) radius, so is it a body? HOTmag (talk) 13:55, 1 October 2024 (UTC)[reply]

The problem is that you are using concepts from classical physics: region; radius; density; location; space; time. The whole point (ha!) is that a black hole is thought to contain a Gravitational singularity, where classical geometries, physics and mathematics, and the relationships that govern them, break down because infinities are involved. We truly do not know what lies within the event horizon of a black hole, even whether space and time, or spacetime, have meanings there (if there even is a there, there). Until we achieve a successful theory of Quantum gravity, we cannot describe the situation even mathematically, let alone in words, and cannot visualise or conceptualise it. {The poster formerly known as 87.81.230.195} 94.6.86.81 (talk) 22:38, 1 October 2024 (UTC)[reply]

Since we can attribute some properties to a black hole, like a mass (and other properties), the situation is not that obscure, despite the infinities. Further, if it had been that obscure, we couldn't have claimed anything about a black hole, not even that it emits a Hawking radiation, or that a black hole "shrinks" when it emits that radiation. But our article black hole does claim a black hole shrinks, and my question was, how do we know the shrinkage also refers to the size and not only to the mass, i.e. what's wrong in a scenario where the black hole's mass decreases while the black hole's size remains constant. My main question (in my original post) only refers to this scenario, provided that it's really possible. Is it? HOTmag (talk) 11:25, 2 October 2024 (UTC)[reply]

The only black hole parameter we're aware of that could possibly be considered its size is its Schwartzschild radius, which is proportional to its mass. So if it loses mass, it shrinks, if we're willing to make any statements about its size.

There's in GR no hidden parameter for the size of a body inside the event horizon, even less a prediction of what might happen if such a hypothetical body gets outside the event horizon. GR is however quite clear that any matter present within the event horizon must move towards the centre (we've no way to check), so no extended body can remain just inside the event horizon for a long time. It's also clear that at the centre, the theory breaks down. When enough of the black hole has evaporated in Hawking radiation to make quantum gravity matter, who knows? PiusImpavidus (talk) 17:58, 2 October 2024 (UTC)[reply]

Well it is an astronomical body. But body there does not mean something just like a billard ball but larger. Like body also doesn't mean it must be like a cadaver or the collective members of church or the main flavour of wine or the main text of a book or lots of other things it is applied to. It is a general word for a concept and not all astronomical bodies are the same in detail. NadVolum (talk) 22:58, 1 October 2024 (UTC)[reply]

When I say "body", I mean something that has a mass located in some region characterized by an (average) radius. Something like a stellar black hole. That's why my question affords to use the term "body". HOTmag (talk) 11:25, 2 October 2024 (UTC)[reply]

We don't know that a black hole shrinks, because we have not yet been able to observe the phenomenon, or observe Hawking radiation itself. But – the theories that include these predicted phenomena seem to successfully accord with what measurements and phenomena we can observe directly or firmly deduce. Perhaps next year someone will come up with an even better theory, or next century we will be able to make direct observations that prove or disprove the current theory. At the moment, however, this is the best we can do.

Further to my earlier remarks, you are implying that by measuring a black hole's mass (fairly easy) and its radius (less easy) from external observations we can calculate its density: this assumes that it has the same volume internally as we observe externally, but we cannot assume this because it's not necessarily classical (or even relativistic) in there – maybe it's 'bigger' on the inside than on the outside; maybe it has two, or four, or five spacial dimensions; maybe it has two time dimensions. All bets are off because 'singularity'. {The poster formerly known as 87.81.230.195} 94.6.86.81 (talk) 14:22, 2 October 2024 (UTC)[reply]

Worth mentioning here that "radius" doesn't have exactly its usual meaning in this context. It's the circumference divided by 2π, not the "distance to the center" in any usual sense. "Circumference" itself also takes some explanation, which I'm not sure I could give correctly. --Trovatore (talk) 22:56, 2 October 2024 (UTC)[reply]

Notice that under current conditions of the universe, stellar mass (and larger) black holes do not shrink due to Hawking radiation. They do emit it, but at a black body temperature that is lower than that of the cosmic microwave background. In other words, they gain more mass from the CMB than they lose due to Hawking radiation. This will reverse as the universe expands and the CMB cools down, but it will be a couple billion years under most current models. If there ever were very small primordial black holess, or if a Romulan warbird lost control of its quantum singularity, those might have radiated away. --Stephan Schulz (talk) 14:48, 8 October 2024 (UTC)[reply]

Does it really reverse? As the CMB cools down at the same time it feeds the black holes. The then more massive black holes cool down too in their Hawking radiation. Does the CMB ever catch up with the black holes? Or is there a permanent difference in temperature? Making living near black holes forever possible. 176.0.148.153 (talk) 13:15, 13 October 2024 (UTC)[reply]

The black hole is a particularly nasty construct from a theoretical standpoint. Assume that flat space is constructed from cubes a Planck length in size. Now curvature is represented by making the sides of the cubes inequal. If you do that, the size of the cubes approaches zero as you go near the event horizon. So inside the event horizon literally no space exists and a black hole is really a hole in spacetime.

That viewpoint, that I have described in the last paragraph is indistinguishable from a viewpoint where spacetime inside a black hole exists but can not be observed. 2A02:3032:305:F2EF:616E:4B30:D3CA:B0AE (talk) 20:14, 3 October 2024 (UTC)[reply]

Gin a black hole kiss a black hole / need a black hole cry? --Trovatore (talk) 20:00, 2 October 2024 (UTC) [reply]

I think the straightforward answer to "Must a given body, that has just been a black hole, always remain a black hole, as long as the body exists?" is it is very likely that a black hole stays being a black hole as long as it exists. However we have never actually observed one yet going out of existence. And there's no theory I know of which entertains the idea of a big but nearly massless black hole. NadVolum (talk) 14:28, 4 October 2024 (UTC)[reply]

Why must a nearly massless black hole be big? 176.0.164.84 (talk) 14:21, 6 October 2024 (UTC)[reply]

Because of assumption #2 in the question, which is an invalid assumption according to current theories which state that nearly massless black holes cannot be big. Sean.hoyland (talk) 14:27, 6 October 2024 (UTC)[reply]

Not true! Assumption #2 only calls for constant size, not for constant big size. What if the size of the body (whatever that means) is small from the start? 176.0.164.84 (talk) 02:44, 7 October 2024 (UTC)[reply]

You are right. I assumed your question was in response to the statement "And there's no theory I know of which entertains the idea of a big but nearly massless black hole." because it quotes from it and I treated 'big' as a proxy for initial radius in the context of mass loss in the OP's question. Either way, the size of the boundary that separates the not-black-hole from the black-hole space-time regions is a function of the mass. Sean.hoyland (talk) 05:09, 7 October 2024 (UTC)[reply]