## Is there a maximum mass for a black hole?

 Quote by mfb 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.
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?
 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.

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[QUOTE]no calculations here, just logic:

QUOTE]

As far as I can tell no a single statement you imagine is correct. I'm not saying there is no 'logic' in your thinking, in fact I can't make any sense of much of that post, but it seems you are extending classical analogies to relativistic black holes. That doesn't apply. It won't work.

Are you aware spacetime inside a black hole becomes very distorted.....that is very, very curved. So you can't use classical measures of time and distance. Those are based on Eucledean space and a typical BH is described by Schwarzschild coordinates.
The volume of a BH is NOT the classical 4/3[pi]r3.....nor is the surface area the classical 4[pi]r2 There is generally believed to be NO matter inside...although some may be infalling at a particular time. Did you know the curvature of a charged BH is different from that of one with no charge...because of the additional energy of an electromagnetic field.

Are you aware the absolute BH horizon begins to grow before matter reaches it? Are you aware that the 'radius' inside a BH is a time dimension, not a distance. That the singularity is a point in time not in space? Are you aware the relative horizon jumps discontinuously with changes in matter/energy? That a newborn BH exhibits violent, chaotic tidal oscillations of a BKL singularity...and these gradually disappear as the BH ages?

These are all things I don't think are available by any convenient logic; they flow from mathematical models of GR.

Here are a few descriptions I keep to remind me how strange BH actually are:

Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)

 The flow of time slows to a crawl near the horizon, and beneath the horizon time becomes so highly warped that it flows in a direction you would have thought was spacial: it flows downward towards the singularity. That downward flow, in fact, is why nothing can escape from a black hole. Everything is always drawn inexorably towards the future, and since the future inside a black hole is downward, away from the horizon, nothing can escape back upward, through the horizon.
Black Hole Complementarity
Leonard Susskind, THE BLACK HOLE WAR (his arguments with Stephen Hawking)

 (p238) Today a standard concept in black hole physics is a stretched horizon which is a layer of hot microscopic degrees of freedom about one Planck length thick and a Planck length above the event horizon. (p258) From an outside observer’s point of view, an in falling particle gets blasted apart….ionized….at the stretched horizon…before the particle crosses the event horizon. At maybe 100,000 degrees it has a short wavelength and any detection attempt will ionize it or not detect it!
 http://www.jimhaldenwang.com/black_hole.htm {Inside the horizon:} It is the coordinate with the minus sign that determines the meaning of “timelike. Notice how the minus sign has moved from the t coordinate to the r coordinate. This means that inside the event horizon, r is the timelike coordinate, not t. .... According to GR, inside a black hole, time is defined by the r coordinate, not the t coordinate.
In fact horizons are spheres of coordinate timelike singularities not ones of classical volume.

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 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.
This is probably the best short answer to the original question.

Near the end of the universe, when things are empty and cold, and entropy is nearing a maximum, there may be several/many BH remaining. These will gradually disappear via Hawking radiation...because individual BH are not repositories of maximum entropy...so they will be unstable....

On the other hand it seems most of these BH will be causally disconnected at some point.....very far apart....so maybe their Hawking radiation will simply dissipiate as does the CMBR currently...and eventually in a flat universe:

 ...... in the heat death scenario, the energy density is so low that the system can be thought of as non-gravitational, such that a state in which energy is uniformly distributed is a thermal equilibrium state, i.e., the state of maximal entropy.
http://en.wikipedia.org/wiki/Heat_death_of_the_universe

but apparently this is one of a number of possible scenarios; Anyway, we won't be there to see which one happens!!

[QUOTE=Naty1;4025027]
 no calculations here, just logic: QUOTE] As far as I can tell no a single statement you imagine is correct. I'm not saying there is no 'logic' in your thinking, in fact I can't make any sense of much of that post, but it seems you are extending classical analogies to relativistic black holes. That doesn't apply. It won't work. Are you aware spacetime inside a black hole becomes very distorted.....that is very, very curved. So you can't use classical measures of time and distance. Those are based on Eucledean space and a typical BH is described by Schwarzschild coordinates. The volume of a BH is NOT the classical 4/3[pi]r3.....nor is the surface area the classical 4[pi]r2 There is generally believed to be NO matter inside...although some may be infalling at a particular time. Did you know the curvature of a charged BH is different from that of one with no charge...because of the additional energy of an electromagnetic field. Are you aware the absolute BH horizon begins to grow before matter reaches it? Are you aware that the 'radius' inside a BH is a time dimension, not a distance. That the singularity is a point in time not in space? Are you aware the relative horizon jumps discontinuously with changes in matter/energy? That a newborn BH exhibits violent, chaotic tidal oscillations of a BKL singularity...and these gradually disappear as the BH ages? These are all things I don't think are available by any convenient logic; they flow from mathematical models of GR. Here are a few descriptions I keep to remind me how strange BH actually are: Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,) Black Hole Complementarity Leonard Susskind, THE BLACK HOLE WAR (his arguments with Stephen Hawking) In fact horizons are spheres of coordinate timelike singularities not ones of classical volume.
Well I am not trying to model black holes I am just playing with ideas. You can humour me or not but I am just experimenting. I simply need a method of calculating a density and acceleration away from a point within that density.
 I have found a page at superstringtheory.com that gives me what I need. Can anyone help in getting an understanding of this. I have no idea how I would translate this into code to produce data that can be graphed. http://www.superstringtheory.com/blackh/blackh1a.html Better still is there already a graphical representation.
 Can anyone tell me if the following statement from the above site is true. "For a planet the mass of the Earth, this distance is only about a centimeter. So if the Earth were less than a centimeter in diameter, the escape velocity at the surface would be greater than the speed of light."

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 Quote by hubble_bubble Can anyone tell me if the following statement from the above site is true. "For a planet the mass of the Earth, this distance is only about a centimeter. So if the Earth were less than a centimeter in diameter, the escape velocity at the surface would be greater than the speed of light."
Without doing the math it sounds about right.

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 Quote by hubble_bubble I have found a page at superstringtheory.com that gives me what I need. Can anyone help in getting an understanding of this. I have no idea how I would translate this into code to produce data that can be graphed. http://www.superstringtheory.com/blackh/blackh1a.html Better still is there already a graphical representation.
What exactly do you want to graph?

This website seems a little silly; just looking at it, the author for some reason writes Newtonian gravity in arbitrary D dimensions, then just states the Einstein equations and the schwarzschild solution in D=4... OK. Nothing is flat out wrong, it's just strange (especially since nothing on this page has anything to do with superstring theory).

 Quote by Nabeshin What exactly do you want to graph? This website seems a little silly; just looking at it, the author for some reason writes Newtonian gravity in arbitrary D dimensions, then just states the Einstein equations and the schwarzschild solution in D=4... OK. Nothing is flat out wrong, it's just strange (especially since nothing on this page has anything to do with superstring theory).
Sometimes discoveries are made by mistake. Maybe he may make the right mistake. :-)

I want to plot density of a mass against the calculated escape velocity. As stated above does a 1 cm earth have an escape velocity that is greater than the speed of light? If so I would assume it has an event horizon. This would technically be equivalent to a black hole, but the mass is too small. I just want to play with the figures to see where I end up. I am not interested in modeling the real universe at this stage. I just want to examine different avenues in related areas. Tweaking the variables in novel ways can bring to light possibilities that have not been taken into consideration.

I would like to graph the density of a spherical mass against the escape velocity at various distances from the centre of said object. So this would be a series of graphs.

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 Quote by hubble_bubble I want to plot density of a mass against the calculated escape velocity. As stated above does a 1 cm earth have an escape velocity that is greater than the speed of light? If so I would assume it has an event horizon. This would technically be equivalent to a black hole, but the mass is too small.
No, it would not be too small, it would be a bona fide black hole. (The figure of 1cm is roughly correct)

There is no minimum mass (except for, perhaps, the Planck mass) for a black hole, and as I already stated no [clear] maximum mass. Everything in between is obtainable. Of course, all of the ones which are not ~solar mass to billions of solar masses don't appear to be realized in nature, but that's not really the point.
 Recognitions: Gold Member Science Advisor It appears you may be under the impression that matter density [pressure] effectively increaes rest mass, due to mass-energy equivalence. This is untrue. The effective mass of a black hole, or condensed matter object, is the same as its uncompressed progenitor mass.

 Quote by Chronos It appears you may be under the impression that matter density [pressure] effectively increaes rest mass, due to mass-energy equivalence. This is untrue. The effective mass of a black hole, or condensed matter object, is the same as its uncompressed progenitor mass.
No I know the mass is the same. It is simply in a smaller volume. What I meant was, as the last poster pointed out, is that earth mass is too low to collapse naturally into a black hole. That is not the point of what I am attempting. I want to start from a simple premise. At the point I have the basic information I need I will be applying that elsewhere.
 How about minimum mass for black holes caused by gravitational collapse. Isn't it something like three solar masses?
 Mentor 3 solar masses is the mass limit for the star in the calculations, the remaining black hole would have a lower mass (I think something like 2 solar masses?). However, no black holes of this size were detected yet, so this is a bit speculative.

 Quote by mfb 3 solar masses is the mass limit for the star in the calculations, the remaining black hole would have a lower mass (I think something like 2 solar masses?). However, no black holes of this size were detected yet, so this is a bit speculative.
I assume you mean that the other mass is ejected before or during the collapse.

I am looking at a modified Schwarzchild calculation for the data I need. I want to work in the effects on time too. The fact that e=mc2 leads onto a calculation where c becomes negative and mass compression becomes a component. What does mass compression do to energy levels? Could energy form around a singularity. As you have the event horizon could you have another band near the singularity where time is running at a comparable rate to that of light elsewhere and light itself is stationary?

Imagine a collision of particles within the event horizon. this initiates an energy release in the form of a photon which wants to head toward the event horizon. It will be impossible for the photon to do this. The particle is no longer "experiencing " light as it normally acts. As light may now appear static, time may take its place in the environs of a singularity. Now if c is zero this makes no sense. If c however is negative then this may indicate that time is negative, but this is not necessarily so. If time was negative then particles would be attracting light rather than emitting it. This would indicate an increase in energy which is counter intuitive near the singularity.
 Have a think about this. "Objects in a gravitational field experience a slowing down of time, called time dilation. This phenomenon has been verified experimentally in the Scout rocket experiment of 1976 [2], and is, for example, taken into account in the GPS system. Near the event horizon, the time dilation increases rapidly. From the point of view of an external observer, it takes an infinite amount of time for an object to approach the event horizon, at which point the light coming from it is infinitely red-shifted. To the distant observer, the object, falling slower and slower, approaches but never reaches the event horizon. The object itself might not even notice the point at which it crosses the event horizon, and will do so in a finite amount of proper time." This postulation must be false. If everything falling into a black hole appears to take an infinite amount of time to reach the horizon these things would be lit up like christmas trees. Not exactly black. So if one million spacecraft were sent into the event horizon we would see 1 million static spaceships around the horizon for ever. Discussion welcome.

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