Why does a black hole get bigger when it consumes mass?

[Mark Lees]

My very basic understanding of black holes leaves me with a question about why black holes increase in size, or rather, why does the event horizon increase in size.

As I understand it, a black hole is a large amount of mass condensed into a such a small space that the amount of gravity produced overwhelms light (and anything else).

This, as far as I understand, means that If the mass increases then so does the amount of gravity.

But, if gravity increases then surely the black hole would become more compact, i.e. smaller due to the extra "pull".

I can see how adding stuff to something "should" make it larger. That appears common sense but the event horizon, as I understand it, isn't something that the mass is added to, it's added to the "stuff" inside the black hole, i.e. beyond the horizon..

Could someone help me with my understanding without throwing the swarzchild radius at me (or if you do, please explain in laymans terms).

Regards
Mark.

 

[Orodruin]

The event horizon is not something you can touch physically, nor does it represent the region in which the mass is concentrated. (In fact, the Schwarzschild solution assumes there is no mass anywhere where it is applicable - which excludes the singularity at r=0)

Instead, the event horizon is the boundary of the region from which nothing can leave the black hole. More mass means stronger gravitational effects, leading to this region - and therefore its boundary - expanding.

 

[Nugatory]

Could someone help me with my understanding without throwing the swarzchild radius at me (or if you do, please explain in laymans terms)

Set aside general relativity and black holes for a moment, and just consider a ball of lead one kilometer across and a ball of feathers one kilometer across. Clearly the ball of lead is much heavier, much denser, and much more compact. It also has much stronger gravitational field because of its greater mass - at any given distance its gravitational effects will be stronger than those of the ball of feathers. Now suppose we had a one kilometer ball of some material even more dense and compact than lead; it will be even more massive and its gravitational effects will be even greater at any given distance.

Throwing more mass into a black hole has the effect of making the mass at the center greater so that its gravitational effects are felt at greater distances. The event horizon, which is what we generally think of as the surface of the black hole, is one of those gravitational effects so the greater the mass the greater the distance at appears and the larger the black hole is.
(One caution - the "surface" of the black hole and the "distance" from the center to the event horizon are somewhat bogus concepts. They're OK for this explanation, but you'll have to unlearn them at some point as you learn more).

 

[PeterDonis]

As I understand it, a black hole is a large amount of mass condensed into a such a small space that the amount of gravity produced overwhelms light (and anything else).

No, that's not what a black hole is. A black hole is a vacuum inside--at least, it is except for a very short period of time when it first forms by the collapse of some massive object, before the collapsing object forms a singularity at the center and disappears*, leaving only spacetime curvature behind. That spacetime curvature is what a black hole is made of, and what traps light so that it can't escape.

the event horizon, as I understand it, isn't something that the mass is added to, it's added to the "stuff" inside the black hole, i.e. beyond the horizon.

No; as above, there is no "stuff" inside the black hole, only vacuum. Anything that falls in past the horizon continues falling until it reaches the singularity, where it disappears.*

The reason the horizon expands when things fall in is that that's how spacetime curvature behaves. There isn't really a simple intuitive way to see how this works, because a black hole doesn't work like the simple intuitive ordinary objects you're used to. Orodruin's and Nugatory's explanation of "stronger gravitational effects" might be as good a simple view as you're going to get, even though it has limitations (some of which Nugatory hinted at--another is the fact, as I've said above, that a black hole isn't an ordinary object made of "stuff" and doesn't work like one).

* - Here I am using the standard classical GR model of a black hole, where quantum effects are ignored. Most physicists think that, when quantum effects are included, something different will happen where the classical theory says there is a singularity. We don't have a good theory for what that something different is, but whatever it is, it won't affect the subject of this thread, so I've taken the simple step of ignoring it.

 

[martinbn]

No, that's not what a black hole is. A black hole is a vacuum inside--at least, it is except for a very short period of time when it first forms by the collapse of some massive object, before the collapsing object forms a singularity at the center and disappears*, leaving only spacetime curvature behind. That spacetime curvature is what a black hole is made of, and what traps light so that it can't escape.

Is that really the case? Or do you have a specific solution(s) in mind? If it is the case in general is there an easy argument that shows it or is it more difficult than that?

 

[PeterDonis]

Is that really the case? Or do you have a specific solution(s) in mind?

Certainly, the Schwarzschild solution, which describes a black hole, is a vacuum solution. The Oppenheimer-Snyder solution, which describes a spherically symmetric collapse to a black hole, has a Schwarzschild vacuum region "glued" at a boundary (which represents the surface of the collapsing object) to a collapsing FRW region (which is not vacuum since it describes the collapsing matter). The O-S solution is what I was describing; the Schwarzschild vacuum region in this solution describes the black hole, as I said, for all but the very beginning of its history (when it is formed from the collapsing object), and since it's vacuum, it has nothing in it but spacetime curvature, so that's all it can be made of.

 

[martinbn]

Yes, I know that, I was guessing that you had OS in mind. But is this a feature for all black holes? No assumption on symmetries nor on the matter that collapses to form the black hole.

 

[PeterDonis]

is this a feature for all black holes? No assumption on symmetries nor on the matter that collapses to form the black hole.

Classically, it is the case that all black holes, regardless of symmetries, will have singularity at the center that everything that falls in will end up hitting, and thus disappearing. The singularity theorems of Hawking and Penrose proved this with no assumptions about symmetries (Hawking & Ellis is the classic reference). They did make assumptions about the matter: they assumed that it satisfied certain energy conditions. So "matter" that violates those conditions--which is called "exotic matter" because nobody knows whether it can actually exist, at least at a classical level (quantum is another matter, see below)--could theoretically avoid forming a singularity. But no matter that anyone has actually observed violates the energy conditions.

Quantum mechanically, it is possible for certain quantum field states to have expectation values for their stress-energy tensor that violate the energy conditions. The simplest example is vacuum energy, which is called "dark energy" in cosmology. In cosmology, the effect of vacuum energy is to create a sort of "repulsive gravity", that makes the expansion of the universe accelerate instead of decelerate. In black hole physics, the effect of vacuum energy is Hawking radiation: black holes can lose mass, and in principle at least, can eventually disappear, along with the singularities inside them. But, as I noted in post #4, all of that is irrelevant to the question in the OP, which is asking what happens when something falls into a black hole; for any black hole of stellar mass or larger, the effect of Hawking radiation is utterly negligible. (In fact, if we take the CMB into account, no stellar mass or larger black hole is even emitting Hawking radiation, because the temperature of the hole is lower than the temperature of the CMB; even if no matter is falling in, the hole is absorbing radiation from the CMB, not emitting it.)

 

[martinbn]

The singularity theorems show that there will be singularities (under the assumptions, which are fine), but they don't say anything about the nature of the singularity, not even if it will be space-like or not.

 

[PeterDonis]

The singularity theorems show that there will be singularities (under the assumptions, which are fine), but they don't say anything about the nature of the singularity, not even if it will be space-like or not.

That's true, but the singularity theorems also don't apply just to black holes. They apply to any spacetime that meets the conditions. (For example, they show that the standard FRW spacetimes used in cosmology must have an initial singularity.)

If we are talking about black holes, then we are talking about the Kerr-Newman family of spacetimes. We know the nature of the singularities in all of those spacetimes. It is true that not all of them are spacelike--only the Schwarzschild one is. However, that is also the only one for which we have a model of how the hole could be formed by gravitational collapse: the Oppenheimer-Snyder model of a spherically symmetric collapse to a Schwarzschild hole. We do not have a known model for how any other type of hole could be formed by gravitational collapse.

Furthermore, all of the black hole interiors in the Kerr-Newman family are unstable to small perturbations. (In fact, the Kerr interior has an "infinite blueshift" at the inner horizon, so any small perturbation will create infinite spacetime curvature at the inner horizon. I think the Reissner-Nordstrom interior has a somewhat similar problem at the inner horizon, but I'm not certain of that.) The Schwarzschild spacetime is also the only black hole solution for which we have an alternate interior that is stable against small perturbations: the BKL solution. (The Wikipedia page describes a universe with an initial BKL singularity, but the time reverse of this is a possible interior solution for a black hole formed by an approximately spherically symmetric collapse.) This solution has the same properties as the O-S model that I described.

So I guess the best answer to your question of whether the properties I described apply to all black holes is "we're not sure". We know they apply to holes that are formed by approximately spherically symmetric gravitational collapse. But we don't know enough about the actual interiors of other types of holes, or even how they could form by gravitational collapse, to say anything definite.

One property that is shared by all black holes, though, is that they are made of spacetime curvature. The Kerr-Newman solutions are all vacuum solutions. All the uncertainty about interiors that I mentioned above does not affect that; at most, it affects the details of the original collapsing matter that forms the hole, and possibly the details of the spacetime curvature well inside the interior. But that doesn't change the fact that if you're thinking of a black hole as an ordinary object with "stuff" in it, and matter falling into the hole as "adding stuff" the way you would to a ordinary object to make it larger, you're thinking of it wrong.

 

[martinbn]

But that doesn't change the fact that if you're thinking of a black hole as an ordinary object with "stuff" in it, and matter falling into the hole as "adding stuff" the way you would to a ordinary object to make it larger, you're thinking of it wrong.

Couldn't agree more with that. It also applies to thinking about the geometry inside, it is not like the interior of a sphere and so on