Does Increasing Density Increase Gravity?

[gaurav_shade]

Keeping the mass constant, if we go on increasing the density of a body
its gravity also goes on increasing, like what happens in a black hole,O.K.?

But according to the formula F=Gmm/r(square) , only the mass of the 2 bodies is taken into consideration...
Suppose 2 spheres are kept at a fixed distance,there would be a certain force acting
along their centres...
Now, keeping distance{r} and their masses
constant if we increase their density,
the gravitational force would obviously increase,
but if we use the formula we would still get the previous result, as the mass and
distance are still the same

in simpler words...
suppose two stars are revolving a around a common centre of mass,
as most of them do...neither sucks the other's gas...

but, if one of them them becomes a black hole, it would start sucking the other
{as you already know, that's how they are detected}

Conclusion:- Although the mass remains same{decreased to be precise,as the outer layers are shed off}, its gravity shows a substantial rise.

If I were to shrink this Earth to suitable volume{hypothetical},it would become a black hole and start sucking the sun itself.

 

[EL]

Keeping the mass constant, if we go on increasing the density of a body
its gravity also goes on increasing, like what happens in a black hole,O.K.?

No, the strength of the gravitational field outside a body does not depend on the body's density. In other words, it doesn't matter wheter the body is a black hole or not.
For example, the solar system planets would move in exactly the same orbits if the Sun was switched for a one solar mass black hole.

 

[D H]

Now, keeping distance{r} and their masses constant if we increase their density, the gravitational force would obviously increase

The gravitational force remains constant in this case. In classical physics, for all points outside of some spherical body of mass M, the gravitational force caused by the body is exactly the same as if the body were replaced by a point mass of mass M located at the center of the spherical body.

 

[russ_watters]

in simpler words...
suppose two stars are revolving a around a common centre of mass,
as most of them do...neither sucks the other's gas...

but, if one of them them becomes a black hole, it would start sucking the other
{as you already know, that's how they are detected}

Conclusion:- Although the mass remains same{decreased to be precise,as the outer layers are shed off}, its gravity shows a substantial rise.

If I were to shrink this Earth to suitable volume{hypothetical},it would become a black hole and start sucking the sun itself.

The cosmological vacuum cleaner is a popular bastardization of what a black hole is. But they aren't: if the Sun were to suddenly be replaced with a black hole of equal mass, our orbit would not be affected at all.

Now, keeping distance{r} and their masses
constant if we increase their density,
the gravitational force would obviously increase,

I notice you don't have an equation that shows that. Why do you believe it to be true?

 

[gaurav_shade]

all i want to ask is that
wont the increase in density cause a bigger bend in space-time,
and isn't this bending of space-time called gravity...

 

[HallsofIvy]

all i want to ask is that
wont the increase in density cause a bigger bend in space-time,
and isn't this bending of space-time called gravity...

Then you SHOULD have asked that instead of simply asserting that it was "obviously" true! Although you did not ask that question intially, it as answered: No! Increasing density, as long as the mass remains constant doesn't change gravitational force (nor the "bend" in space-time) at a fixed distance from the center of the object: the gravitational force between two objects depends upon their masses and the distance between them, not upon their densities.


Of couse, in order to increase the density while keeping mass constant, you will have to decrease the size of the object- that will make it possible for other objects to be closer and that decreased distance would increase the gravitational force- that's what happens with a black hole.

 

[tripz16]

HallsofIvy if u decrease the size of the object in order to increase the density without altering the mass wouldn't how would it be possible for other object that were previously at one distance be closer? if u decrease the size then they are still the same distance from the center of the main object we are talkin about and the gravitational force would remain the same. am i right? i was just a lil confused about last post

 

[dilletante]

HallsofIvy if u decrease the size of the object in order to increase the density without altering the mass wouldn't how would it be possible for other object that were previously at one distance be closer? if u decrease the size then they are still the same distance from the center of the main object we are talkin about and the gravitational force would remain the same. am i right? i was just a lil confused about last post

Without speaking for H of I, I suspect he was pointing out the following:

The closest you can bring an object to the center of mass of the Earth for example is about 4,000 miles, the radius of the earth. If you squeezed the Earth down to a body with a radius of 2,000 miles, the same object on the Earth would experience a greater gravitational force because the centers of the two masses would be closer together. If you squeezed the Earth into the density of a black hole, the gravitational force near the black hole would be stronger still. However, if the object was 4,000 miles from the center of the black hole it would experience the same gravitational force as the original object sitting on the original earth.

 

[gaurav_shade]

well then
why does the gravity of black hole increase,
after all the mass even 'decreases' as the outer layers are shed off,
and it is only the density that increases...
and gravity does increase as it starts sucking the companion star

and the distance{r} between them{2 stars} certainly does not decrease,
cause 'r' is the distance between their of masses...
and in case of spheres it remains at the same place
no matter what you do to its volume

 

[russ_watters]

well then
why does the gravity of black hole increase,

It doesn't. That's what we're telling you.

It might help if you could tell us where you are getting these ideas of yours. Are they conclusions you drew based on popular science descriptions of black holes? These ideas of yours are wrong.

 

[gaurav_shade]

well i got the idea from the fact that
when the wannabe black hole is a star, it doesn't suck the other star's gas
but when it becomes one, it literally rips the star apart{exagerrating}

 

[DaveC426913]

A star orbiting another star of mass M at distance D will not be bled of its gas.

Likewise, that same star orbiting a BH of mass M at distance D will also not be bled of its gas.

However, in the second case, the star's orbit can decay so that it is closer to the BH, and that THAT point, it will start losing its gas to the BH.

Note also, there are lots of cases where stars bleed other stars. Blue dwarfs often bleed their red giant companions.

 

[russ_watters]

There are also other reasons why stars may bleed companions. If one star turns into a red giant, its outer layers might be pushed close enough to be pulled into its companion, for example.

 

[tripz16]

ok i got another question then ... if a black hole is formed and it has a certain mass and it sucks in other objects will the mass of the black hole increase or will the density increase or what? what happens to the things that are sucked in?

 

[Chris Hillman]

What happens to stuff which falls into a black hole?

if a black hole is formed and it has a certain mass and it sucks in other objects will the mass of the black hole increase or will the density increase or what?

The mass will increase (according to gtr). "Density" is a tricky notion in strongly curved spacetimes, so I suggest we avoid that.

what happens to the things that are sucked in?

According to gtr? This question has been an active topic of research for decades. By definition, an observer inside the hole can't send his findings off to arxiv.org, so it raises a philosophical challenge to the Baconian explanation of the methods and goals of science. Still, we can ask what gtr says about it. The simplest way to study this question is to see what happens in some idealized models of black holes, such as the Schwarzschild or Kerr vacuum solutions to the Einstein field equation which governs gtr. Then, the short answer is that stuff which falls into a black hole gets "spaghettified" (drawn into a long thread oriented radially) by tidal forces, and also compacted in terms of volume (before you ask, yes, it still makes sense to speak of density of small objects!).

A longer answer is that if you look at more elaborate models which take account of the perturbing effect of radiation (starlight) and matter (gas pulled off a partner star in a binary system, for example), then while the exterior of a black hole is very well modeled by the Kerr vacuum, the interior should be quite unlike the interior of the "external Kerr hole". There should be a "strong spacelike curvature singularity" and anything which gets close to that will be sphagettified and crushed, but there might also be a "weak singularity"; anything which manages to avoid the strong singularity would encounter the weak singularity. Interestingly enough, it is possible that objects might survive this encounter, not because the curvature doesn't blow up (it does, at least in some models) but because in a sense this might happen too quickly for the object to respond by being torn apart or crushed. In such a case, gtr itself declares "after this, I don't know what happens". This picture goes by the name of "Poisson-Israel" model, BTW; it is based on some approximations, not exact solutions (realistic ones are generally too complicated to write down).

An even longer answer might continue something like this: at extremely high curvatures, or equivalently extremely large mass-energy densities, physicists expect gtr to break down, with unknown consequences. Some physicists expect that when a workable quantum theory of gravity appears, it might turn out that curvature singularities (which are unavoidable according to gtr in many circumstances--- there are rigorous theorems to this effect, but they assume that gtr is always fully correct, which physicists expect cannot be quite true) may be replaced with something more subtle. Or they may not. It's important to realize that many things you might read about are speculations, possibly even wild speculations. For example, in another thread, someone asked about the possiblity that the interior of black holes might turn out to harbor "baby universes" (certain simple exact solutions known as de Sitter or Nariai lambdavacuums have been suggested as components of possible models). However, it seems fair to say that these are playful speculations with no observational support and questionable theoretical support.

Fans of gravitational waves will no doubt be intrigued to hear that some nifty mathematical machinery developed in order to construct exact solutions which model "colliding gravitational plane waves" yielded an unexpected connection with black hole interiors. Roughly speaking, the outer half of the interior of Schwarzschild or Kerr solution (the part which should remain fairly accurate) is locally isometric to part of an appropriate "CPW" model! This raises the intriguing possibility of that we could get a better idea of what happens inside a black hole if we could make strong gravitational waves and watch them collide. Alas, pretty much the only objects which appear capable of making strong gravitational waves are... black holes!

 

[gaurav_shade]

@dave
you said
"the star's orbit begins to decay"

doesn't increase in gravity a reason for that phenomena...

-
gaurav

 

[Janus]

@dave
you said
"the star's orbit begins to decay"

doesn't increase in gravity a reason for that phenomena...

-
gaurav

Since the gravity of the star doesn't increase, it isn't. A reason a stars orbit might decay is through friction with the material the collapsing star threw off during its process of collapse.
The main reason you see black holes "stealing" matter from another star has already been mentioned. Sometime since the collapse, the second star reached the red giant stage of its life cycle and expanded. As it expands it grows beyond its Roche lobe which is the point at which tidal forces from the collapsed star are strong enough to pull away material. This is not due to any increase in the collapsed star's gravity, the same would have happened if the expansion had happened before the collapse. Again, as has already been pointed out, there are plenty of examples of non-collapsed stars drawing material away from a close companoin.

 

[gaurav_shade]

@Janus

Alright alright i get the point
No need to use those 'offensive' quotes...

I learned about space-time through the analogy of a trampoline...
The bend in trampoline was compared gravity ...

So i simply thought that maybe if we were to concentrate
the entire mass to the centre, the 'trampoline' would bend considerably more
and thus resultantly 'increase gravity'

I guess a little learning is truly a dangerous thing

 

[aman malik]

this thing is purely hypothetical and makes no sense(sorry to say) at all. you mean thet every object in this world can become a black hole. if i am wrong try explaining me again.

Keeping the mass constant, if we go on increasing the density of a body
its gravity also goes on increasing, like what happens in a black hole,O.K.?

But according to the formula F=Gmm/r(square) , only the mass of the 2 bodies is taken into consideration...
Suppose 2 spheres are kept at a fixed distance,there would be a certain force acting
along their centres...
Now, keeping distance{r} and their masses
constant if we increase their density,
the gravitational force would obviously increase,
but if we use the formula we would still get the previous result, as the mass and
distance are still the same

in simpler words...
suppose two stars are revolving a around a common centre of mass,
as most of them do...neither sucks the other's gas...

but, if one of them them becomes a black hole, it would start sucking the other
{as you already know, that's how they are detected}

Conclusion:- Although the mass remains same{decreased to be precise,as the outer layers are shed off}, its gravity shows a substantial rise.

If I were to shrink this Earth to suitable volume{hypothetical},it would become a black hole and start sucking the sun itself.

 

[Chris Hillman]

Many posters have pointed out various problems with various things the OP said. But for what it is worth:

you mean thet every object in this world can become a black hole. if i am wrong try explaining me again.

Consider a lump of clay. It has some fixed mass m and some average density [itex]\rho[/itex], which is increased if one places the clay in a strong bag and squeezes in a vise. You can imagine compressing the lump of clay, so that its density is greatly increased. Indeed, researchers can change flakes of graphite into diamonds this way!

According to gtr, in principle, if you could compress the lump of clay into a small enough ball, it would indeed undergo complete gravitational collapse and form a black hole.

 

[DaveC426913]

According to gtr, in principle, if you could compress the lump of clay into a small enough ball, it would indeed undergo complete gravitational collapse and form a black hole.

...though it would mantain the same gravitational pull on nearby objects as the orignal lump of clay, which is so small as to be barely measurable.

 

[OSalcido]

...though it would mantain the same gravitational pull on nearby objects as the orignal lump of clay, which is so small as to be barely measurable.

This bothers me... I thought the reason super massive black holes existed was because they sucked in the matter around them and since galactic centers have an abundance of matter... the black hole was able to grow to millions of times the sun's mass. If black holes don't "suck", how can million solar mass bhs exist? The initial black hole wouldn't have any greater gravity than the star it was born from, in fact it would have less! Since its not sucking in any more than its star-form... other mass/stars falling into the black hole would be less likely than a star colliding with its star-form.. and since we don't see a million stars coalescing in the galactic center... how can these super massives be explained?

I was always under the impression that black holes were drains in space where not only matter was sucked down, but time and space itself... since that would cause the space in the vicinity around the black hole to shrink.. it would add to the gravitational effect from its mass

can someone shed any insight?

 

[Nereid]

orbital decay, in gtr

While two massive objects orbiting their common centre of mass may be stable under Newtonian gravity, they are not in gtr - energy is radiated from the system in the form of gravitational (wave) radiation. Hulse and Taylor got the Nobel in physics, in 1993, for their observations of a binary neutron star with an orbit decaying just as the doctor (Einstein) ordered!

Note that there is an indirect link between the density of two such mutually orbiting massive objects and the rate of orbital decay. However, this link arises because the mutual orbits of very dense objects can be much, much smaller (e.g. tens or hundreds of km vs thousands or millions of km) - two stars, each the mass of the Sun, cannot orbit each other at a distance of 500 km, for example, while two neutron stars can, quite easily!

 

[DaveC426913]

This bothers me... I thought the reason super massive black holes existed was because they sucked in the matter around them and since galactic centers have an abundance of matter... the black hole was able to grow to millions of times the sun's mass. If black holes don't "suck", how can million solar mass bhs exist?

How is this a dispcrepancy? As you swaid, there's lots of matter in the centre of the galaxy. It's inb the form of stars but much of it is also in the form of dust and gas. And it's all unstable orbitwise. So dust, gas, stars and planets alike fall in and bvecome part of the BH's mass.

I think the key here is understanding how close everything is at the core and how unstable.

 

[Chris Hillman]

Trying yet again to explain the point

I thought the reason super massive black holes existed was because they sucked in the matter around them and since galactic centers have an abundance of matter... the black hole was able to grow to millions of times the sun's mass. If black holes don't "suck", how can million solar mass bhs exist?

DaveC and I are trying to explain that gravity works the same way for a black hole as it does for any other object of the same mass. That is, black holes don't "suck" any harder than anything else, they are just more compact. The point is that the gravitational field of any object becomes stronger the closer you get.

As it happens, neutron stars are also very compact (not quite as compact as black holes), yet they can be thought of as genuine "objects" with a solid surface. So it should help to compare the gravitational effect of a neutron star and an ordinary star on nearby matter. Because a neutron star is more compact than an ordinary star with the same mass, you can get a lot closer to it without striking the surface, so you can experience much stronger gravitational fields outside the surface of a neutron star than outside the surface of an ordinary star.

I was always under the impression that black holes were drains in space where not only matter was sucked down, but time and space itself... since that would cause the space in the vicinity around the black hole to shrink.. it would add to the gravitational effect from its mass

I don't know what this is supposed to mean, but if you think that the gravitational fields of objects other than black holes behave fundamentally differently from the gravitational fields of black holes, that is wrong--- in a sense, the whole point of gtr was to elegantly capture the principle that gravitation affects all bodies the same way and is also produced by all forms of mass-energy the same way.

 

[Nereid]

This bothers me... I thought the reason super massive black holes existed was because they sucked in the matter around them and since galactic centers have an abundance of matter... the black hole was able to grow to millions of times the sun's mass. If black holes don't "suck", how can million solar mass bhs exist? The initial black hole wouldn't have any greater gravity than the star it was born from, in fact it would have less! Since its not sucking in any more than its star-form... other mass/stars falling into the black hole would be less likely than a star colliding with its star-form.. and since we don't see a million stars coalescing in the galactic center... how can these super massives be explained?

I was always under the impression that black holes were drains in space where not only matter was sucked down, but time and space itself... since that would cause the space in the vicinity around the black hole to shrink.. it would add to the gravitational effect from its mass

can someone shed any insight?

To address the 'history' aspect of your questions ... (others have addressed the 'gravity' parts well already).

The origins of the SMBH found in the nuclei of many (most?) galaxies is an active area of research, and AFAIK there are few firm results yet. One reason why is that the early universe - between the time of the last (photon) scattering and, say, objects with redshift of 5 - is extraordinarily difficult to observe.

However ...

How (SM)BHs 'feed' is somewhat understood - via accretion disks, in which the 'mechanics of eating' (so to speak) include properties of (baryonic) matter - collisions of particles, radiation, magnetic fields, and so on. However, the details of these disks are poorly understood, partly because they are far too small to be resolved in any astronomical observation.

How matter comes to get close enough to an SMBH that it can join the accretion disk is also somewhat understood - the bars in spiral galaxies seem to play a role, as do collisions between galaxies.

At a sufficiently high level, the 'accounting' seems to work: the luminosity history of the SMBHs - as AGNs, whether quasars, Seyferts, BL Lac objects, etc; i.e. the stuff around the SMBH, the accretion disk, the jets, the dust torus, etc - is consistent with the evolution of galaxies and the expansion of the universe ... at least back to z ~ 3 or 4.

 

[Chronos]

It is clear that galactic core SMBH's snack on nearby matter, but, it is not clear that is how they originated. It is plausible they were already enormous, and may played a major role in the formation of their 'host' galaxy.

 

[DaveC426913]

It is clear that galactic core SMBH's snack on nearby matter, but, it is not clear that is how they originated. It is plausible they were already enormous, and may played a major role in the formation of their 'host' galaxy.

I think it is not unreasonable - for the purpose of the poster's question - to model galaxy accumulation analagous to solar system formation. In a rotating mass of dust and gas, it will tend to accumulate in the centre (actually, it will transfer its kinetic energy out of the system by way of escaping mass, leaving the remaining matter with less, causing it to accumulate near the centre). Caveat: I'm not suggeasting this is actually how galaxies form, I'm only trying to demonstrate how mass accumulates in the centre of a gravitational well without the need of a BH to explain it.

So: regardless of whether there's BH at the centre, mass will accumulate there. Thus, when there IS a BH there, the BH will be eating the infalling mass. We now have a model that makes sense in that the BH is able to continually eat the mass of the galaxy, but is not actually "sucking" the matter in.