# Is there a maximum mass for a black hole?

1. Jul 21, 2012

### rogerperkins

I recently tried to calculate the mass of the black hole in the center of the milky way and it came out to 1.8x10e+53 kg, that can't be right, what's going on?

Last edited: Jul 21, 2012
2. Jul 21, 2012

### Nabeshin

Well your calculation is very wrong, since the mass of the black hole is actually something like $10^{37}$ kg.

But in short, no there is no theoretical maximum size for a black hole, except for perhaps the sum of all the mass energy in the observable universe.

3. Jul 22, 2012

### Drakkith

Staff Emeritus
How did you calculate it?

4. Jul 22, 2012

### jetwaterluffy

Did you try to calculate the mass with newtonian physics? Calculating black holes without general relativity can run into problems.

5. Jul 23, 2012

### rogerperkins

Oops, I found an error in my original calculation . New calculation gives me about 2e41. Yes, I only used newtonian physics, thought about relativistic effects, but not sure what those would be or how to calculate. I ignored any effects from the mass in the rest of the galaxy, not sure if that's significant. I also ignored any decay in the orbit of the sun. I used wikipedia to get most of the values. Here is my calculation:

F = G (m1 m2 / r^2)
F = ma
a = G (m / r^2)
G = 6.674e-11 N m^2 / kg^2
r = 8.3 kpc
1 parsec = 3.0856802e16 m
r = 2.561e20 m

Vsun = 230,000 m/s
a = v^2 / r
a = 2.066e-10 m/s^2

m = a r^2 / G
m = 2.030e+41 kg

Thanks!

Last edited: Jul 23, 2012
6. Jul 23, 2012

### Nabeshin

It is! You wouldn't necessarily know it from just doing a naive calculation, though. The SMBH is in reality something like $10^7 M_{\odot}$, while the galaxy as a whole is something like $10^{11} M_{\odot}$, so most of the gravitational pull on the sun that would factor into the calculation you've just done is coming from normal (and dark) matter, not the black hole in the center.

To get the mass of the black hole you have to use the orbit of something much much closer to the black hole, so that you're ensured that the majority of the gravitational force is due to it. This is precisely what is done!

7. Aug 1, 2012

### morghen

no calculations here, just logic:

Starting from the, considered true, fact that the black holes occupy space(like other compacted matter objects, stars, neutron stars):

black holes also have a range of mass, why? they express themselves via a volume(area) of space so that means that there is something holding contents of the black hole into a structure that occupies space. If it did not have a maximum mass it would simply be an infinetely small point being able to absorb everything, something like reverse big-bang.
i dont buy the "matter cant be compacted any further" statement...we have clear evidence that it was..

8. Aug 1, 2012

### Drakkith

Staff Emeritus
The diameter of the black hole is usually considered to be where the event horizon is. This is not a "structure". It is simply the distance from the center of the black hole that the gravitational strength becomes great enough to keep light from leaving. We don't know what is behind the event horizon, specifically whether there is an actual singularity or if that is simply a mathematical error that stems from our lack of knowledge about it.

9. Aug 1, 2012

### morghen

So you're saying the observable diameter of the object has no corelation to its mass?
You're satisfied with "simply the distance from the center of the black hole to the event horizon" ?

Even if the event horizon is just a shell around a point with zero/one volume, what's behind the EH is probably not empty, but accelerating material that has passed the event horizon and it is heading towards the maximum gravity point...so there must be a flowing structure.

If however the black hole is a solid globe of compressed matter that occupies space then there must be a critical mass point.

10. Aug 1, 2012

### Staff: Mentor

The Schwarzschild radius is proportional to its mass.
While this is not appropriate close to black holes, if you calculate a "volume" and a "density", it decreases for larger black holes.

Where is the problem?

It is not, at least not with the Schwarzschild radius. And it does not matter how it looks inside. The event horizon is just a result of GR in a region where GR is valid.

11. Aug 1, 2012

### Drakkith

Staff Emeritus
No, the more massive a black hole is the larger the diameter of the event horizon.
Yes.

I would not call infalling material a "flowing structure".

What is this critical mass point?

12. Aug 2, 2012

### morghen

hehe, this is a bit like saying: god went click and the light was on :P

why not? what would you call it? or you think it just infalls without any rules/properties?

why are you being sarcastic? how should i know? but if the black hole occupies any space at all there probably is a certain mass value after which there come changes within/out the black hole.
Why would you believe the black hole is such a rigid and ultimate concept?

13. Aug 2, 2012

### Drakkith

Staff Emeritus
What are you talking about? We have defined the diameter of a black hole to be this way, I can't see a relation between your statement here and the diameter of a black hole.

The infalling material is in free fall unless it collides with other infalling material, just like it does outside of the black hole, and it should obey the same rules, at least up to a certain point. I don't know where the rules would begin to break down. If you want to call this a structure, then feel free.

I'm not. I actually just now realized what you were talking about.

Maybe. It's possible a quark star or other exotic stellar remnant could form an event horizon. If more mass is added that star may then collapse into something else. We simply don't know yet.

Please, don't put words in my mouth, I have said nothing of the sort.

14. Aug 2, 2012

### morghen

Sorry for that, just trying to push a bit on fact that you said: Yes after i asked if you're satisfied with answers like "simply the distance from the center of the black hole to the event horizon" when it comes to whats beyound the event horizon.

i would really like to see theories on how the material travels after the event horizon.

15. Aug 2, 2012

### Chronos

A black hole, in theory, has another 'structure' inside the event horizon called the Cauchy horizon, and has another 'structure' outside the event horizon called the photon sphere. We obviously have no direct knowledge of how matter behaves inside the event horizon because ... it's inside the event horizon. According to theory, it is merely disassembled and and absorbed by the singularity after it passes the event horizon.

16. Aug 6, 2012

### hubble_bubble

Has anyone ever tried to calculate escape velocity during a stellar collapse. There would be an initial escape velocity due to the mass of the star before collapse. what would be the escape velocity for a neutron star for instance? Or a red dwarf? How would you actually calculate such values?

17. Aug 7, 2012

### Staff: Mentor

Similar to all other objects, if you neglect relativistic effects. $v=\sqrt{\frac{2GM}{r}}$ where M is the mass inside for spherical mass distributions. For neutron stars, it might be useful to add some relativistic corrections, but the formula gives a good approximation.

18. Aug 7, 2012

### hubble_bubble

What about matter compression? To plot the velocity when the compression approaches singularity the increased compression needs to be included. How would the equation be modified to account for this?

19. Aug 7, 2012

### hubble_bubble

I have found a wikipedia article here.

http://en.wikipedia.org/wiki/Escape_velocity

The second equation under the heading "Calculating an escape velocity" has p for average density but this may be inadequate for my purposes.

20. Aug 7, 2012

### Naty1

Last edited: Aug 7, 2012