# About gravity and black holes

1. Nov 14, 2004

### Ryosuke

Here's another one of my stupid ideas :tongue2:

First question, do black holes have a finite mass or an infinite mass?

If they have a finite mass, disreguard everything i write below.

Now if they have infinite mass, the gravitational formula is:

Gravitational force = (G * m1 * m2) / (d2)

so, blah blah blah, it would mean the gravitational force of the black hole was infinite too, which couldn't be true, could it?

2. Nov 14, 2004

### Integral

Staff Emeritus
The mass of a black hole is finite.

3. Nov 15, 2004

### Ryosuke

should teach me to pay more attention

4. Nov 16, 2004

### primal schemer

Is there any way of knowing the mass?? I thing I read somewhere (I may be wrong) that the mass (and gravity) of a black hole is roughly equal to that of the star before it turned into a black hole. Is this correct???

5. Nov 16, 2004

### arildno

In order for a star to turn into a black hole, its mass must exceed some value (which I don't know).
To go out on a limb here (I don't know much about this, either), the basic dynamics for the formation of a black hole is that through burn-off of its matter, the star reaches a point where it cannot generate the necessary pressure to prevent the collapse of its form into a black hole.
(The gravitational force on an element of the star is directed inwards to the center, hence all elements would speed inwards to the center unless a sufficient pressure kept them from doing so..).

6. Nov 16, 2004

### rayveldkamp

Well its about greater than 30 times the mass of the Sun that a black hole forms. A black hole is formed when matter achieves a density such that the escape velocity is greater than the speed of light. We can only know exactly 3 quantities of a black hole namely the mass, charge and angular momentum...all other information of what made it up is lost (related to entropy...but thats a whole other long and complex story!!)
As for the mass query it is NOT constant....Hawking found that black holes can lose energy, by particles escaping. Particle-antiparticle pairs can be formed at the event horizon by energy from the gravitational field, if one of the pair falls into the black hole the other continues until infinity, i.e carrying energy away from the blackhole-this is known as Hawking Radiation.
Hope this helps

Ray

7. Nov 16, 2004

### arildno

rayveldkamp:
Do we have, as yet, any estimate of the rate of energy loss of the black hole due to Hawking radiation other than that it is probably non-zero?

8. Nov 16, 2004

### rayveldkamp

The answer is not exactly, but we can make a very good approximation. We currently have no quantum theory of gravity, but we do for the other fundamental interactions, so to explain black holes we use the quantum theories of these three, but use Einstein's General Relativity (a CLASSICAL theory) to account for gravity...this is OK because the quantum gravity effects only take place on very very small scales, namely the Planck lenght 10^-35m

At any instant the energy of the black hole is given by E=mc^2. A rather crude approximation is to equate the derivative of this to the Stefan-Boltzmann law, and after a little integration we get the result that for a black hole the same mass as our Sun it would take 10^66 years to completely evapourate.
So the answer to your question is a VERY small rate of energy loss, however the amazing result is that there is an "evapouration" of black holes.

9. Nov 16, 2004

### theriddler876

but if light has an escape velocity, wouln't that mean that it also has mass?, for example you have to be going faster than 9.8 to escape earth, and the more massive the object, the more energy you need to reach this.

10. Nov 16, 2004

### rayveldkamp

No, in the quantum model light consists of photons which are massless particles, but do exhibit wave-like phenomena (eg light diffraction, reflection etc), nonetheless light is particle in nature. Photons, although having no mass, do have a momentum, this is why light has an escape velocity.
Since the photon is massless it must travel at the speed of light c, and hence it is a relativistic particle and cannot be treated with the usual methods. The energy is given by:
E^2=p^2 c^2 +m^2c^4 where p is its momentum and c is its REST MASS.
Hence for a photon (or any massless particle) E=pc

Hope this helps
Ray

11. Nov 16, 2004

### AnthreX

is black hole 3 dimensional ?

12. Nov 16, 2004

### rayveldkamp

ahhh its hard to say, on the basis of our everyday space-time we would say it is 4 dimensional (3 space + 1 time), however many theories, for example some superstrings and M-theory predict the universe consists of many more dimensions than just 4. So the answer is simple...we dont know!