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Author Topic: Is there a maximum possible mass size  (Read 2224 times)

Offline jeffreyH

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Is there a maximum possible mass size
« on: 24/02/2014 06:18:27 »
Considering escape velocity from an object we see this is related to the mass size and increases in proportion to that mass. Following this there must be a critical mass at which an uncompressed object will have Ve = c. Could there be massive objects of this sort. If there were we simply would not see them as no light would escape. What would this mass size actually be? Is it impossible for anything to get this big?


 

Online evan_au

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Re: Is there a maximum possible mass size
« Reply #1 on: 24/02/2014 07:54:07 »
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Could there be massive objects of this sort.
Such objects are predicted by the work of Laplace, Einstein, Chandresakar and Hawking - today we call them black holes.
Studies of the motion of stars in eliptical orbits near the center of our galaxy strongly suggest that there is a black hole at the center of our galaxy. Astronomers are hoping for a more detailed look this year, as a cloud of gas circles this mysterious object.

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Is it impossible for anything to get this big?
Chandrasekhar calculated that a white dwarf larger than about 1.4 times the mass of the Sun would collapse into a black hole. We see a number of stars in this category, and infer that there would have been many in the past. So it seems almost certain that black holes exist (in theory).

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What would this mass size actually be?
A black hole 10 times the mass of the Sun would be about 30km diameter, although those at the center of a galaxy could be larger than the solar system.

We may have discovered some of them already, as supernovae or X-Ray binary stars - but we cannot easily distinguish between a neutron star and a black hole companion in a binary star system.

Recent theoretical analysis looking at bursts of radiation from the inside edge of an accretion disk may allow us to eventually distinguish black holes and neutron stars by the relativistic effects in this intense gravitational field.
 

Offline jeffreyH

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Re: Is there a maximum possible mass size
« Reply #2 on: 24/02/2014 11:06:27 »
I think you may have missed my point. I am not talking about collapsed objects but objects of a size where Ve = c. This is different to a black hole which has to compress to rs in order to create an event horizon. As the escape velocity increases with mass size there comes a point where a mass is so large that Ve at the surface reaches c. These objects would not be high density. The question is, is this situation even possible? Would collapse naturally occur at mass sizes much lower than this theoretical limit? I may run some numbers to determine the exact value for this limit. Personally I believe this situation is impossible to reach.
 

Online evan_au

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Re: Is there a maximum possible mass size
« Reply #3 on: 24/02/2014 15:26:58 »
Sorry if I under-estimated your question...

Chandrasekhar's calculations showed that the center of a large object like a non-rotating star is far more compressed than material near the surface. He showed that long before the surface gravity reached c, the material near the center would be so compressed that no force known (at the time) could withstand the star collapsing to within the Schwarzchild radius rs.

We now know that the the rather stolid neutrons, and the normally rather ghostly neutrino particles are able to act on the extremely dense in-falling matter, and rescue some of a star's mass from being swallowed by a black hole.

Current theories suggest that stars beyond 50 solar masses will collapse directly to a black hole without a supernova, while stars in the range 20-50 solar masses will form a black hole during a supernova; below 20 solar masses, the supernova will produce a neutron star. But the calculations are extremely difficult.

It is conceivable that a neutron star (millisecond pulsar) which is being spun up by infalling matter from a companion star could reduce the compression in the center sufficiently that it doesn't collapse until somewhat above this limit.

It sounds reasonable that more diffuse objects like galactic dust clouds are unlikely to achieve the densities necessary for the surface escape velocity to exceed c. Parts of the cloud would first need to collapse to supermassive stars.
 

Offline jeffreyH

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Re: Is there a maximum possible mass size
« Reply #4 on: 24/02/2014 22:30:34 »
I have just done some calculations and found some very interesting results. For instance a dense enough gas cloud of the right mass can trap light. During the early stages of the big bang light could not outrun the initial expansion and time was basically frozen as the mass expanded at the shock wave. This will change or has changed and it may be light itself that is driving expansion. I will post a couple of graphs later to illustrate the point.
 

Offline jeffreyH

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Re: Is there a maximum possible mass size
« Reply #5 on: 24/02/2014 23:15:54 »
The graphs below were generated using a modified version of Ve = SQRT((2GM)/r). The re-arranged equation M =  = (f(Ve)^2*f(r))/(2G) was derived to vary either Ve or r to find various values for mass, radius and density. The graphs here were both generated with Ve = c as escape velocity. Density here drops and approaches zero density at infinity. It has a knee whose value has not yet been determined. I am still pondering implications of this data. I will update this post later with more observations.

One quick update. This data shows that Ve = c at every value of rs (Schwarzschild radius). The density drop off should balance with gravitational feedback as the volume of the sphere containing the mass grows through each successive rs value. This has implications for the mechanism that drove the big bang.
« Last Edit: 24/02/2014 23:20:37 by jeffreyH »
 

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Re: Is there a maximum possible mass size
« Reply #5 on: 24/02/2014 23:15:54 »

 

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