Do black holes technically have less net gravity than the original star?

[Fanghur]

I've been curious about this for a while, so correct me is I'm wrong. Black holes are often thought of as having more gravity than any other object in the universe, but a little while ago it occurred to me that this technically should not be true. Gravity is directly proportional to an object's mass If I'm not mistaken. And black holes are formed when a massive star goes supernova, effectively blowing a great proportion of its mass out into space. So with that in mind, wouldn't a black hole technically speaking have less net gravity than the original star did? To be sure that gravity would be far more 'concentrated' that that of the original star, but in terms of NET gravity possessed by the black hole, would it be fair to say that it has less gravity in that sense?

[beefpatty]

I've been curious about this for a while, so correct me is I'm wrong. Black holes are often thought of as having more gravity than any other object in the universe, but a little while ago it occurred to me that this technically should not be true.

 

You are correct, that is not true. What makes them so strong is that you can get very, very, very close to the center of gravity. Since the strength of gravity is proportional to 1/r^2, where r is the distance from the center of gravity, you can see as the distance gets close to zero the strength blows up to infinity. If the Sun were to suddenly turn into a black hole, we'd still rotate around it all the same.

Edited February 9, 2013 by beefpatty

[elfmotat]

Since the strength of gravity is proportional to 1/r^2, where r is the distance from the center of gravity

 

Newtonian gravity is not very accurate when you're close to a strong field source like a black hole. The rough equivalent of the Newtonian "g" value actually blows up to infinity at the event horizon.

[zapatos]

I've been curious about this for a while, so correct me is I'm wrong. Black holes are often thought of as having more gravity than any other object in the universe, but a little while ago it occurred to me that this technically should not be true.

A black hole is a mass that is sufficiently compacted to create an event horizon. Black holes come in many sizes, ranging from that of a few solar masses, all the way up to billions of solar masses.

 

You are correct that a black hole that forms from a stellar explosion is smaller than its original star. If you were distance 'x' from a star that exploded then collapsed into a black hole, you would notice less gravity after the star became a black hole.

 

Some black holes are indeed the most massive objects in the universe (depending on how you define 'object'), but since black holes can exist in various sizes, not all black holes would be considered amongst the most massive objects.

[SamBridge]

I think perhaps gravity in a black hole you have a greater degree of curvature at it's surface, I remember there was equations to calculate the distortion in space to calculate time dilation that actually used trigonometric functions and approaching black holes they can warp past 360 degrees at some point, whereas a star may not, but can still have a greater range of high gravity.

[ajb]

I've been curious about this for a while, so correct me is I'm wrong. Black holes are often thought of as having more gravity than any other object in the universe, but a little while ago it occurred to me that this technically should not be true. Gravity is directly proportional to an object's mass If I'm not mistaken. And black holes are formed when a massive star goes supernova, effectively blowing a great proportion of its mass out into space. So with that in mind, wouldn't a black hole technically speaking have less net gravity than the original star did? To be sure that gravity would be far more 'concentrated' that that of the original star, but in terms of NET gravity possessed by the black hole, would it be fair to say that it has less gravity in that sense?

What do you mean by net gravity?

 

But yes, when a star forms a black hole some of the star's initial mass will be lost in a supernova.

[Fanghur]

You are correct, that is not true. What makes them so strong is that you can get very, very, very close to the center of gravity. Since the strength of gravity is proportional to 1/r^2, where r is the distance from the center of gravity, you can see as the distance gets close to zero the strength blows up to infinity. If the Sun were to suddenly turn into a black hole, we'd still rotate around it all the same.

In practice, however, that does not actually happen though, correct? I mean, if for example we were able to somehow drill our way to the exact center of the Earth, the gravitational force wouldn't actually become infinite?

 

So then would it be fair to say that, if comparing space-time to an infinitely-elastic 'sheet', that a black hole would effectively be a tangent (i.e. tan(90) ) in that sheet? Or am I looking at this too literally?

[elfmotat]

In practice, however, that does not actually happen though, correct? I mean, if for example we were able to somehow drill our way to the exact center of the Earth, the gravitational force wouldn't actually become infinite?

 

So then would it be fair to say that, if comparing space-time to an infinitely-elastic 'sheet', that a black hole would effectively be a tangent (i.e. tan(90) ) in that sheet? Or am I looking at this too literally?

 

At the center of the Earth all of the mass is around you, so the net gravitational field is actually zero. What's unique about a black hole is that all of its mass is concentrated in a very small volume.

[Fanghur]

What do you mean by net gravity?

 

But yes, when a star forms a black hole some of the star's initial mass will be lost in a supernova.

I was making an analogy wherein I compared the strength of a gravitational field to a chemical solution; in the original star (solution), the volume was incredibly large and so the gravity (chemical) was spread out over an extremely large area. When the star became a black hole, however, all that gravity became compressed into an infinitesimally small volume, and thus became far more 'concentrated'. Does this analogy make sense?

[moth]

The missing factor is density. If you packed the mass of the Earth into a region of space smaller than the Schwarzschild radius then you get a black hole.

Not just by moving close to the center of gravity of a mass.

[elfmotat]

The missing factor is density. If you packed the mass of the Earth into a region of space smaller than the Schwarzschild radius then you get a black hole.

Not just by moving close to the center of gravity of a mass.

 

You actually only need to compress it to 9/8 its Schwarzschild radius to ensure collapse.

[moth]

You actually only need to compress it to 9/8 its Schwarzschild radius to ensure collapse.

Interesting point. Is that after the electrons have been expelled, or is there another reason for the collapse?

[elfmotat]

Interesting point. Is that after the electrons have been expelled, or is there another reason for the collapse?

 

The internal pressure required to "counteract" gravity approaches infinity as the radius of a spherical object approaches R=9GM/4c².

[moth]

That makes sense, I didn't think it through.

There are Neutron stars, which have no electric charge, that don't collapse to a black hole.

But once enough mass is close enough together, a force that could stop the collapse would have to be infinitely large and so, not possible.

[Przemyslaw.Gruchala]

 

or is there another reason for the collapse?

 

 

Lack of nuclear reaction and fusion.

 

p+ + p+ + some energy -> p+ + n0 + e+

 

proton colliding with other proton with enough kinetic energy can produce proton, neutron and positron. Proton and neutron will join to deuterium.

Other time neutron will again decay to proton, electron and neutrino. Electron and positron will annihilate producing photons.

 

Other combination is:

p+ + e- + some energy -> n0

Proton with electron and some energy will convert to neutron. Which will join with surrounding proton and construct deuterium.

 

Heavy particles are going to core. Lighter particles reverse, to outer areas.

 

This process is making sure that core is not collapsing.

But only until there is enough matter to continue nuclear reaction.

 

[Enthalpy]

Different collapse processes must be distinguished.

 

Any mass is supposed to form a black hole if it becomes concentrated enough, including dark matter. This is not related with nuclear reactions, formation of neutrons or other.

 

As long as a star radiates enough light, radiation pressure prevents it from getting too dense and collapsing into a black hole, which would also need said star to be heavy enough.

 

Smaller stars that have stopped fusion without collapsing to a black hole can make other compact objects. For instance a neutron star, if they have the proper mass.

 

Because most stars have companion(s) and exchange mass, more varied and complicated scenarios occur.

 

-----

 

The total mass of a black hole isn't straightforward because gravitation energy changes during the collapse and this energy is mass...

 

Am I right to believe that all mass added to an existing black hole adds fully to the hole AND its equivalent is radiated as electromagnetic waves and particle jets, so that the added mass "counts twice" as it falls in the gravitation well?

 

And what about the initial mass that creates the stellar black hole: is the hole as heavy as the visible matter not expelled that collapsed? How much energy gets radiated during the collapse: any mass exceeding Schwarzschild counts twice?

 

Thanks!

[suburban]

Newtonian gravity is not very accurate when you're close to a strong field source like a black hole. The rough equivalent of the Newtonian "g" value actually blows up to infinity at the event horizon.

 

i have two questions, 1) what quantity are you refering to when you speak of the equivalent of g ?

2) i'm not saying its wrong but to me it just doesn't sound right that something that wild occurs at the event horizon which has nothing

special about it, it's merely a point in spacetime where one coordinate system fails and another one needs to be applied... are you sure

about what you said ?

 

thx

 

[hadron-12]

The gravity of black holes is definitely stronger than that of stars. No light escapes from a black hole, that is until it reaches critical mass.

[zapatos]

The gravity of black holes is definitely stronger than that of stars. No light escapes from a black hole, that is until it reaches critical mass.

That depends on from where you are measuring the gravity, and the sizes of the black hole and the star. If our sun suddenly became a black hole with no loss of mass, there would be no change in gravity from our perspective.

 

A five solar mass black hole would have 'less' gravity than a six solar mass star.

[elfmotat]

1) what quantity are you refering to when you speak of the equivalent of g ?

 

 

I'm talking about the proper acceleration (i.e. what you would measure with an accelerometer) an observer experiences if he maintains a constant [math]r[/math] value:

 

[math]a=\frac{GM}{r^2 \sqrt{1-2GM/c^2r}}[/math]

 

 

On Earth we maintain a constant [math]r[/math] value because the ground holds us in place. If you plug in the mass and radius of Earth, you get ~9.8 m/s². Notice that when [math]r\gg 2GM/c^2[/math] the square root term is approximately one, so it reduces to the familiar Newtonian value:

 

[math]a=\frac{GM}{r^2 \sqrt{1-2GM/c^2r}}\approx \frac{GM}{r^2}[/math]

 

The square-root term only has a significant effect when you're near the Schwarzschild radius, and it causes proper acceleration to blow up to infinity at the event horizon.

 

2) i'm not saying its wrong but to me it just doesn't sound right that something that wild occurs at the event horizon which has nothing special about it, it's merely a point in spacetime where one coordinate system fails and another one needs to be applied... are you sure about what you said ?

 

You only experience that acceleration if you "hold station." It should intuitively make sense, because once you cross the horizon the radial coordinate becomes timelike and you must always fall towards the singularity. I.e. no amount of acceleration will keep you from falling in. If you free-fall into the BH then you experience nothing strange as you cross the event horizon.

Edited February 20, 2013 by elfmotat

[hadron-12]

That depends on from where you are measuring the gravity, and the sizes of the black hole and the star. If our sun suddenly became a black hole with no loss of mass, there would be no change in gravity from our perspective.

 

A five solar mass black hole would have 'less' gravity than a six solar mass star.

 

 

Ok, I'm talking about an observer that has not crossed, and is a sufficient distance away from, the event horizon. I don't know how you can say that we would not notice a change in g if the sun became a black hole.

 

As for the 5 solar mass BH and the 6 sm star, light could still escape from the star but not from the black hole. The gravity of black holes is infinitely stronger than that of stars. Unless there is something else contributing to the immense gravity of black holes, they must have more mass.

[zapatos]

Ok, I'm talking about an observer that has not crossed, and is a sufficient distance away from, the event horizon. I don't know how you can say that we would not notice a change in g if the sun became a black hole.

 

As for the 5 solar mass BH and the 6 sm star, light could still escape from the star but not from the black hole. The gravity of black holes is infinitely stronger than that of stars. Unless there is something else contributing to the immense gravity of black holes, they must have more mass.

Gravity decreases with distance from the center of mass. The reason we would not notice a difference if our sun suddenly became a black hole of equal mass is because we would still be the same distance from the center of mass of either one.

 

Gravity increases the closer you get to the center of mass. If we took a trip toward the sun, the gravitational pull on us would continue increasing as we got closer and closer. But the closest we can get to the center of mass of the sun with maximum gravity, is the sun's surface. After that, as we move closer to the center of the sun, some of the mass of the sun is now above us, thus causing gravity to decrease. In fact, if you were in the center of the sun, gravity would cancel out in all directions and you would be weightless.

 

If on the other hand the sun was now suddenly a black hole and we took a trip toward it, the gravitational pull on us would continue increasing as we got closer and closer, just like it did with the sun. And when we got to the distance away from the black hole that is exactly the same distance as we were when we were on the surface of the sun, the gravity would be equivalent.

 

But with the black hole, we can keep getting closer to the center of mass of the black hole before we reach its 'surface'. And as we get closer to the center of mass, the gravity continues to increase. At the point of the event horizon, the gravity is so great that not even light can escape.

[ACG52]

Ok, I'm talking about an observer that has not crossed, and is a sufficient distance away from, the event horizon. I don't know how you can say that we would not notice a change in g if the sun became a black hole.

 

As for the 5 solar mass BH and the 6 sm star, light could still escape from the star but not from the black hole. The gravity of black holes is infinitely stronger than that of stars. Unless there is something else contributing to the immense gravity of black holes, they must have more mass.

The same mass, in a much, much smaller volume results in an immense gravitational field at or near the edge of the volume. But that's because of it's smaller size and much higher density. There's still no more mass than was in the original star. As you move away from the edge, the gravity falls off as the square of the distance and the gravity is just that of total mass.