# Black hole density

How does more compression relate to a stronger gravitational pull. Like, when we say that a black hole is a tiny space that has 20-30 suns compressed in it, how does this increase its density and gravitational pulling power (I'm open to mathematical answers but I prefer a layman type answer for better understanding)

• From a distance, a BH of 20 solar masses has the same gravity as a normal star that size, from the same distance. It has no extra sucking power, although tidal effects get extreme when you get close, simply due to your distance from the centre. Any light or matter that falls into a BH quickly falls to the centre. Pure general relativity says it gets crushed out of existence, but we expect quantum effects to modify that, but the core of a BH will still be tiny, probably smaller than an atom under quantum gravity. – PM 2Ring Apr 16 at 13:27
• When stuff falls into a BH, it gets heavier, so its gravity gets stronger. There's no limit to how much a BF can consume, but if too much stuff tries to fall in at once you get a kind of traffic jam just outside the BH, and since that stuff collides at speeds approaching lightspeed, the collisions are extremely spectacular, emitting huge amounts of radiation across the spectrum, and spewing out collision debris, sometimes more than 1000 lightyears for a big active BH like M87*. – PM 2Ring Apr 16 at 13:33
• I've cut it down to one question, this isn't too broad. – James K Apr 16 at 14:00
• – rob Apr 16 at 15:10
• @PM2Ring "There's no limit to how much a BF can consume" Did he eat everything in the fridge again? – David Richerby Apr 16 at 17:20

We can understand gravity as following a set of mathematical equations called "General Relativity" which were discovered by Einstein (and others) around the start of the 20th century. The same gravitational equations apply to black holes, stars, planets, people, apples etc. These equations are very hard to solve. Fortunately there is a very good approximation, that was discovered by Isacc Newton about 350 years ago.

It says that there is a force between any two objects that is proportional to the mass of the each object and inversely proportional to the square of the distance between the objects. The closer the objects are to each other, the stronger is the gravitational force. For normal objects (like you, and an apple) the size of this force is so small that it is almost undetectable. But if one of the objects is very big (like a planet) then it becomes a very strong force.

So if you get a couple of balls of styrofoam. They have some mass and so there is a force of gravity between them. But because they are not very dense they cannot come very close together. If you crush the styrofoam, you make it more dense. This would let you get the balls closer together, and so the force of gravity on the surface would be larger. If you don't push the balls closer together then the force between the balls would stay the same. It is the distance between the masses that is important.

If you have a ball of any matter, there will be some gravitational force pulling it together. If the object is very big, its only gravity will pressurise the centre of the object. For example, the centre of the Earth is under very high pressure, due to the Earth's own gravity.

If it weren't for gravity, the gas that makes a star would fly out into space. What keeps it in one place is gravity - its own gravity. The star is literally compressed by its own gravity, and the pressure is huge. This is due to every atom being gravitationally attracted to all other atoms in the star, they are all pulled together like that - this is what we mean by "the star's own gravity". If the star is massive enough, its own gravity will crush it until it collapses into a neutron star, or even into a black hole.

A star is very massive, and its own gravity would be enough to crush it, if it didn't have a nuclear furnace inside which provides the energy to stop this. But when a star runs out of fuel, its own gravity is enough to crush the core of the star. Since you now have the same amount of mass in a smaller ball, the gravity on the surface is greater.

For a black hole this process runs away (in a way that can only be described accurately by General Relativity). The gravity gets so strong that nothing can prevent the star's complete collapse to a single point (it is a lot weirder than this, because space and time are bent by the mass). Around this is a region of space from which even light can't escape, which is why black holes look black. Furtherout from the black hole, gravity is normal. Black holes don't "suck" they just have strong gravity.

A black hole is not a "hole" in anything. Nor is it a solid object. It is a region of spacetime that is curved so much that nothing can escape this region. All of the actual black holes that we have observed seem to have formed from collapsed stars (there are other ways to make a black hole in theory, but in practice, only stars are massive enough).

None of this answers the question "why does gravity get weaker as distance increases. Perhaps that is due to how gravity spreads out from a mass. It gets weaker in a way that is analogous to how light gets weaker as you get further from a lamp.

Nor does this explain why gravity is proportional to mass. There doesn't seem to be an answer to this (except that in a universe with no gravity, it seems likely that no structures with living creatures could form, so we wouldn't be here to ask the question)

• what do you mean by "the star's "own gravity would be able to crush it?" Gravitational force/ Gravity is always with respect to two forces right? It's like talking about a voltage between two points and not voltage of a point – noorav Apr 20 at 3:42
• @noorav If it weren't for gravity, the gas that makes a star would fly out into space. What keeps it in one place is gravity - its own gravity. The star is literally compressed by its own gravity, and the pressure is huge. This is due to every atom being gravitationally attracted to all other atoms in the star, they are all pulled together like that - this is what we mean by "the star's own gravity". If the star is massive enough, its own gravity will crush it until it collapses into a neutron star, or even into a black hole. – Florin Andrei Apr 20 at 5:08
• @Florin Andrei, I asked PM 2Ring a question in the comments above but I thought I'd ask it here as well so that you get notified. The question is: Is the black hole just like a regular hole that things fall into or is it a solid body that just happens to bend space time so much that it creates a really deep impression on the space time fabric? (I'm using the rubber sheet analogy) – noorav Apr 20 at 12:51
• @noorav It's mostly just warped spacetime, which is just another word for gravity. But yeah, that's pretty much all that a BH is - spacetime, powerfully distorted. The center is very tricky and our theories are incomplete. General relativity says there are all kinds of infinities at the center, which sounds sketchy, but GR is all we have for studying these things. More info: astronomy.stackexchange.com/questions/2240/… – Florin Andrei Apr 21 at 4:08
• General relativity is like a set of equations. The rubber sheet analogy is only an analogy. If you want to understand what it really means, you need to learn the maths. If you have a new question about the rubber sheet analogy you should ask it as a new question, but you should at least read all the answers on physics stack exchange. The rubbersheet analogy causes many misunderstandings. – James K Apr 21 at 7:16

It's simply because you can "get closer" to it, that's all. No special sauce.

You know how gravity is pretty weak far away, and gets stronger close by? The closer you get to the Sun - more specifically to the center of the Sun, because that's how you measure the distance - the greater the pull.

However, once you reach the Sun's surface, there's a problem. As you dive under the surface, the stuff above you, the layers of the Sun you're leaving behind as you keep diving in more deeply, are pulling you in the opposite direction. Part of the Sun is pulling you towards the center as before, but the other part is pulling you up. They fight each other. So gravity actually gets weaker when you dive under the surface.

But what if the Sun was smaller? Same mass, just more compressed. Then you could get closer to it (measured to the center) without diving under the surface (which would weaken the pull). Gravity could get stronger.

Now make it even smaller. You could get pretty freakin' close to it without touching the surface. The pull of gravity could be enormous, and from the same mass, too. It's just that the distance to the center could get smaller before you even touch it, that's what makes the difference.

Black holes are just an extreme example of this. There's no magic, they're just super-tiny for their mass. So you can get very close to them, and gravity just keeps increasing A LOT as you do so. Eventually you reach the event horizon where gravity is so strong that space itself gets weird and you can't get out anymore.

• That last sentence is important! It's not merely that you can't get enough speed or acceleration, the spacetime is curved so much that as you go forward in time you must travel towards the core. There are no paths away from the core, or even paths that keep the same distance. (The only way out is to go backwards in time, and as far as we know that's physically impossible). – PM 2Ring Apr 17 at 5:50
• +1 for a good answer Florin, but that last sentence is wrong. You can plot gravitational potential by plotting the "coordinate" speed of light using a gedanken string of light clocks. The steeper the gradient in gravitational potential at some location, the stronger the gravity at that location. But at the event horizon, the coordinate speed of light is zero, and it can't go lower than that. So there's no more slope. – John Duffield Apr 17 at 12:51
• @JohnDuffield Are you back with crackpot "theories" again? – Florin Andrei Apr 17 at 18:01
• That's not crackpot, Florin. You really can plot gravitational potential with clocks. And see Einstein's 1939 paper on a stationary system with spherical symmetry consisting of many gravitating masses. He said this “g44 = (1 – μ/2r / 1 + μ/2r)² vanishes for r = μ/2. This means that a clock kept at this place would go at the rate zero". A clock can't go slower than that. Google on Oppenheimer frozen star. – John Duffield Apr 18 at 7:37
• @Florin Andrei, how do the layers behind you that you leave behind pull you in the opposite direction? What's the physics behind that? – noorav Apr 20 at 3:44

Black hole has very high gravitational pull not because it is small but because it has huge mass. Gravitational pull does not depend on SIZE but only MASS.

For example is EARTH is compressed to a pebble size( 10 mm in diameter) it will become a tiny black hole. However it will not affect the moon!. Moon will not understand where the earth has gone!. It will remain in the same orbit as before.

• This is true, but one-sided. At the same distance, it's true that only the mass of the central body matters. However, if the body is highly dense, you can get very close to it - and there the gravitational field can get extremely intense in the case of such bodies as black holes. – Florin Andrei Apr 17 at 18:04

Phil Plait:
Black holes can be low density

... the event horizon grows linearly with the mass. In other words, if you double the black hole’s mass, the event horizon radius doubles as well. ...
Density is how much mass is packed into a given volume. Keep the size the same and add mass, and the density goes up. Increase the volume, but keep the mass the same, and the density goes down. ...
A regular black hole — that is, one with three times the Sun’s mass — with have an event horizon radius of about $$9$$ km. That means it has a huge density, about two quadrillion grams per cubic cm $$(2 \times 10^{15})$$. But double the mass, and the density drops by a factor of four. Put in $$10$$ times the mass and the density drops by a factor of $$100$$. A billion solar mass black hole (big, but we see them this big in galaxy centers) would drop that density by a factor of $$10^{18}$$. That would give it a density of roughly $$1/1000$$ of a gram per cc… and that’s the density of air!
A billion solar mass black hole would have an event horizon $$3$$ billion km in radius — roughly the distance of Neptune to the Sun.