# Size of a black hole.

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I got a rather simple question for everyone I was hoping someone would be able to clear up some confusion for me.

I was watching a show on the science channel the other day and they mentioned the super massive black hole in the center of the galaxy. Im in agreeance that it exist but something they said struck me as odd. They stated that the size of the black hole was 15 thousand miles wide.

This is where my current understanding falls apart. Im under the impression that a black hole is a singularity, so how could it have any dimensions other G and spin momentum?

In an effort to not clutter up the forum with small questions I wanted to also ask another quick question. Does anyone know if its possible for a photon to possese gravitation pull. As I understand its rest mass is for all general uses 0 but it forms a small amount of momentum due to the speed that its traveling, evident by the push it is able to excert on objects inspace(see solar sails), meaning that its true rest mass can not be exactly zero. So as an example would anyone be able to tell me what the mass of light would be at say, 100hz.

~Sedit

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Around a black hole there is an undetectable surface called an event horizon that marks the point of no return. It is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect black body in thermodynamics.

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

The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass M through

$r_{sh}=\frac{2GM}{c^2}$

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

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum mechanical effects should describe these actions due to the extremely high density and therefore particle interactions. To date it has not been possible to combine quantum and gravitational effects into a single theory. It is generally expected that a theory of quantum gravity will feature black holes without singularities.

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

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present.

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

In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled "Does the inertia of a body depend upon its energy-content?". The equivalence is described by the famous equation

$E=mc^2$

where E is energy, m is mass, and c is the speed of light in a vacuum.

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. In other words a photon is a little packet of energy which can carry electromagnetic radiation. It is also the force carrier for the electromagnetic force. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has no rest mass; this allows for interactions at long distances. Like all elementary particles, photons are currently best explained by quantum mechanics and will exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when quantitative momentum is measured.

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

The photon is massless, has no electric charge, and does not decay spontaneously in empty space.

...

In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:

$E^2=p^2c^2+m^2c^4$

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

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Yeh that must have been a brain fart, your completely right about the Schwarzschild radius and I cant believe that it didnt cross my mind. Perhaps I was just to wrapped up in a blackhole having dimensions to think about the obvious.

As far as the question about light. Im not sure I understand your explination. Are you saying that you believe a photon truely has zero mass, because I in all honesty don't believe it at all. I have read and understand the text book examples you gave but I thank you non the lest for posting them.

However I have figured that given E=mc2 then it should be able to work the energy content of the photon with E = hc/wavelength and work backwards from E to figure out the mass of the photon. However given that I believe the mass is extremely small it would be next to impossible to use the figures we have now to figure the mass of the photon since a single decimal place off on the speed of light and we would lose the ability to figure for the mass of the photon which would be incredibly small.

What is everyones thoughts on my idea... is it feesable? I worry that the energy of the photon is a measure at the speed of light so how would I take it down to its rest mass energy?

Sorry my post is a little hackish im just rattling off the top of my head at the moment.

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Yeh that must have been a brain fart, your completely right about the Schwarzschild radius and I cant believe that it didnt cross my mind. Perhaps I was just to wrapped up in a blackhole having dimensions to think about the obvious.

As far as the question about light. Im not sure I understand your explination. Are you saying that you believe a photon truely has zero mass, because I in all honesty don't believe it at all. I have read and understand the text book examples you gave but I thank you non the lest for posting them.

However I have figured that given E=mc2 then it should be able to work the energy content of the photon with E = hc/wavelength and work backwards from E to figure out the mass of the photon. However given that I believe the mass is extremely small it would be next to impossible to use the figures we have now to figure the mass of the photon since a single decimal place off on the speed of light and we would lose the ability to figure for the mass of the photon which would be incredibly small.

What is everyones thoughts on my idea... is it feesable? I worry that the energy of the photon is a measure at the speed of light so how would I take it down to its rest mass energy?

Sorry my post is a little hackish im just rattling off the top of my head at the moment.

Photons have relative mass, meaning they have mass because they are equivalent to matter which has mass. In other words, a specific amount of energy is can be a specific amount of matter.

Edited by steevey

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Photons have relative mass, meaning they have mass because they are equivalent to matter which has mass. In other words, a specific amount of energy is can be a specific amount of matter.

So if I understand correctly the general consensus is that they have no true mass but the mass they figure on is only true because the energy could be converted to mass?

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Think of it this way: if you try to match speeds with the photon, by moving in the direction it is traveling as fast as you possibly can, the photon gets red-shifted and thus its energy and relative mass lowered. Now you could say that the mass of things depends on how fast we're going, but we have a perfectly good word for that already: energy. If you measure the mass of something when it is at rest, it is an intrinsic property rather than a relative property, which is more useful. To remove confusion you can say rest mass, which is labeled $m_0$ rather than m, but often it is called mass either way. The other type of mass could be called relative mass or mass-energy or energy to avoid confusion.

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So if I understand correctly the general consensus is that they have no true mass but the mass they figure on is only true because the energy could be converted to mass?

Sort of

Energy is matter, and matter has mass. So as far as I know, photons themselves don't have mass, but they have specific amounts of matter they can be converted into, which will give you some specific amount of mass at any point in time, since the relationship of E=mc^2 isn't known to ever not be true between matter and energy.

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... the super massive black hole in the center of the galaxy.... They stated that the size of the black hole was 15 thousand miles wide.

This is where my current understanding falls apart. Im under the impression that a black hole is a singularity, so how could it have any dimensions other G and spin momentum?

~Sedit

An easy way to comprehend the size of a black hole is imagine the Earth crushed down into a black hole. The event horizon would make the black hole appear to be a flat black ball less than one inch in diameter. Black holes this size and smaller could possibly exist if they were created at the time of the big bang.

The most massive black hole known OJ287 at 18 Billion solar masses (which we should see an outburst in 2015) has a Schw radius of about 4 light days.

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An easy way to comprehend the size of a black hole is imagine the Earth crushed down into a black hole. The event horizon would make the black hole appear to be a flat black ball less than one inch in diameter. Black holes this size and smaller could possibly exist if they were created at the time of the big bang.

The most massive black hole known OJ287 at 18 Billion solar masses (which we should see an outburst in 2015) has a Schw radius of about 4 light days.

I think they measure the size of blackholes solely on where their event horizon is, or how big its mass is which will translate to a certain size for an event horizon.

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