Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: barneyboy on 31/10/2014 21:55:42
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if black holes have/are a singularity of r=0, infinite gravity and matter compressed out of existence, why do all black holes not have the same mass, gravitational pull and event horizon size? if they do not compress matter out of existence they would grow with all the matter they consume but this would mean that the gravity inside the black hole would become zero at its centre, being a perfect sphere. gravity would pull all matter to the black hole, infinite at its surface maybe but it would be a compressive force that would hold it together against the centrifugal force of the high rate of spin from the matter held on the surface by gravity.
In a previous post I asked about the big bang and the singularity, before time, that created the universe , the response I received was that the singularity was not r=0. therefor couldn't have had infinite gravity as there would have been zero gravity at its centre.
if the gravity is not infinite and the black hole continues to grow, there could become a time when the black holes gravity could no longer overcome the force of the spin and cause the black hole to lose its battle of gravity vs all the energy built up inside of it ie strong and weak nuclear force, centrifugal etc.
or the spin to slows sufficiently, due to the increased diameter, for something else to happen. [:P]
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No one knows what is inside a black hole. There are various theories of black holes and an equation to calculate the radius to the event horizon. You may want to read up on this. There is wikipedia for a start. It is interesting.
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if black holes have/are a singularity of r=0, infinite gravity and matter compressed out of existence, why do all black holes not have the same mass, gravitational pull and event horizon size?
I don't understand your question. Why do you think they should have the same mass? Even in Newtonian gravity that would be wrong. Do you know Newton's theory of gravity? It states that if you have a point object of mass M and another point object of mass m then the force magnitude of the force between the two objects is given by
F = GMm/r2
Suppose that M is much greater than m (i.e. M >> m). The force on the second object is F = ma. In this case the acceleration is the acceleration due to gravity wherein we represent a using the letter g, i..e a = g. Then
F = mg = GMm/r2
Cancel out m to get
g = GM/r2
This is the value of the gravitational field at the point r. Notice how it depends on the value of M regardless of it's value and notice also that it's a point object. So why would you think this has to be different for a black hole? Note that the gravitational field far from the black hole has the value g = GM/r2
if they do not compress matter out of existence
No matter can be compressed out of existence.
they would grow with all the matter they consume but this would mean that the gravity inside the black hole would become zero at its centre, being a perfect sphere.
That's not true. At the center the value is undefined (i.e. infinite), not zero. Why do you think it's zero?
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the gravity inside the black hole would become zero at its centre, being a perfect sphere.
This would be true if the black hole were a solid sphere, like the Moon. As you approach the center of the Moon, the gravitational force (or the weight of an object) would approach zero. So if you did manage to tunnel to the center of the Moon without getting crushed, you would be able to float weightless.
We don't really know what is inside a black hole. However, we know of nothing that can withstand the crushing gravity of a black hole. So the black hole cannot be a solid sphere like the Moon. Matter crossing the event horizon is already travelling at a significant fraction of the speed of light. At this speed, it would not take very long to reach the center of the black hole - perhaps microseconds for a stellar-sized black hole, or less than a day for a black hole the size of our galactic black hole.
This suggests that a black hole is mostly empty space, with most of the matter concentrated at the center. So rather than finding a serene zone of weightlessness at the center where you could float without concern, you would smash at immense speed into a zone with extreme tidal forces that would tear you apart - the strength and direction of gravity are wildly different at points only millimetres apart ("spaghettify" is the technical term).
why do all black holes not have the same mass?
The mass of a black hole is determined by how much matter it contains.
If a black hole is formed from the collapse of a small star, it will have less mass than a black hole formed by the collapse of a larger star.
A black hole at the center of a large galaxy has consumed perhaps billions of stars, and has more mass than the black hole at the heart of a smaller galaxy, which has consumed perhaps millions of stars.
why do all black holes not have the same mass, gravitational pull and event horizon size?
A more massive black hole will have a larger gravity, because it has more mass.
A more massive black hole will have a larger event horizon, because the escape velocity from this larger mass will exceed the speed of light further from the center of the black hole. The escape velocity reaching the speed of light is one constraint on the zone from which light cannot escape. There are other constraints on the escape of matter, some of which are affected by the spin of the black hole.
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The Schwarzschild radius to the event horizon rs = 2GM/C^2. Substituting into the equation for escape velocity say for earth we have ve = SQRT(2GMe/rs) where Me = mass of the earth. To get g at the horizon use -GMe/rs^2. We can then plot a graph for both by varying the radius between earth radius down to rs. For a normal earth g =9.80665 m/s^2 and Ve = 11.2 km/s. When we get nearer and nearer the rs value g and ve swap places. g is then a higher value than ve. The physics breaks down because gravitational acceleration would cause a velocity greater than c before the escape velocity reaches c. So things are very strange indeed near a black hole.
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I have attached 2 graphs showing the effect nearing the rs radius of the earth during compression to the event horizon.
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This may be exactly why earth sized masses are unsuitable black hole candidates.
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rs value g and ve swap places. g is then a higher value than ve
I think this comparison is talking about numerical values of the various parameters.
However, you should only compare numerical values when the numbers all use identical units:
- rs, the Schwarzchild Radius: A Length, measured in units of meters (for example)
- ve, the Escape Velocity: A Velocity, measured in units of m/s
- g is the "surface" gravity, measured at the event horizon: An Acceleration, with units of m/s2
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rs value g and ve swap places. g is then a higher value than ve
I think this comparison is talking about numerical values of the various parameters.
However, you should only compare numerical values when the numbers all use identical units:
- rs, the Schwarzchild Radius: A Length, measured in units of meters (for example)
- ve, the Escape Velocity: A Velocity, measured in units of m/s
- g is the "surface" gravity, measured at the event horizon: An Acceleration, with units of m/s2
Acceleration being the rate of change of velocity can be measured at a particular instant. We can establish what the equivalent velocity would be by taking the mean over a small range of values. This gives a localized velocity equivalent. They can be compared in this way by imagining an object starting at the higher position and being allowed to freefall to the lower position. Take the distance over time for comparison. The point was that g will exert a force that would accelerate a freefalling object to light speed at a distance away from the actual event horizon. Everything nearer to the horizon than this has to be considered to be traveling faster than light speed. To me this indicates a missing factor in the equations.
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I read a statement in a book written by, I believe, an astrophysicist (you may or may not agree with his title). it was his statement that said that a blackholes gravity is infinite, that the singularity is a very small point in space and that matter was crushed out of existence.
I understand that if the matter is just compressed, the mass would increase and therefor the event horizon radius would increase but you would in this instance still have surface gravity and decreasing gravity the closer to the centre of mass you got due to the mass surrounding the centre cancelling out as you do with any sphere.
matter passing the event horizon would be accelerated/spaghettified because of the surface gravity to fantastic speeds and be smashed into an extremely hard and compact surface. molecule's can be compressed as they have a lot of empty space, more gravity can compress atoms as they too have a lot of empty space. on a smaller scale is there not also a lot of empty space in the make up of atoms? between the neutrons and protons and a lot of empty space between the up quarks and down quarks that make up neutrons? and so as gravity increases there is a lot of empty space for it to compact into but the physical size will still increase. an increase of size will mean that there is a centre to the sphere that is the "body" of a black hole (the event horizon is the gravitational effect of the body) the larger the "body"/mass the larger the gravitational force at the surface but at the centre it should still be zero, compact but zero gravity. as the mass grows so will the energies trying to blow it apart, all the energies that are being compressed like a balloon. eventually the surface gravity would be overcome by the stored energy and there would be a great big bang.
just because the maths break down why should gravity behave any differently than it does on a smaller scale, forming a sphere, surface gravity and zero centre gravity, compressing matter and fighting against internal energys trying to get out. it may take all the matter in the universe to finally "pop the balloon" but like I said it would be a great BIG BANG.