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[Mentors' note: split off from this thread]
Do all black holes have the same density?
Do all black holes have the same density?
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George Jones said:As mass increases, the density of matter necessary to form a black hole decreases. If fact, if enough stars are used, they don't even have to touch for a black hole to form. In other words the stars have to be close together, but there still can be space between them. Below, I calculate a quantity that I'll call density, but, in reality, the quantity is only suggestive of density.
Setting this "density" to the average density of the sun, about 1400 kg/m^3, gives a black hole mass of about 100 million solar masses. So, if more than 100 million or so (within an order of magnitude) sunlike stars congregate in the centre of a galaxy, they don't have to touch (initially) to form a black hole.
The following calculation is only suggestive, and it is in no way rigorous. Because of the curvature and nature of spacetime, it probably doesn't make sense to calculate the spatial volume inside the event horizon of a black hole.
Density is mass over volume, i.e.,
[tex]\rho = \frac{M}{V},[/tex]
and the volume of a spherical object of radius [itex]R[/itex] is given by [itex]4\pi R^3/3[/itex], so the density of a uniform sphere is
[tex]\rho = \frac{3M}{4\pi R^3}.[/tex]
A spherical black hole has event horizon (boundary) located at
[tex]R = \frac{2GM}{c^2},[/tex]
where [itex]G[/itex] is Newton's gravitational constant and [itex]c[/itex] is the speed of light.
Subsituting this equation into the density equation for a spherical black hole gives
[tex]\rho = \frac{3c^6}{32\pi G^3} \frac{1}{M^2}.[/tex]
The first bit is just a constant number, while the second bit shows that the "density" of a spherical black rapidly decreases as mass increases.
Inverting this equation gives
[tex]M = \frac{c^3}{4}\sqrt{\frac{3}{2\pi G^3}}\sqrt{\frac{1}{\rho}},[/tex]
and using the Sun's density for [itex]\rho[/itex] gives the result I mentioned at the top.
The density of a black hole is not a constant value and can vary depending on the size and mass of the black hole. However, on average, the density of a black hole is extremely high, with some estimates suggesting it can be trillions of times denser than water.
No, the center of a black hole is not a point of infinite density. The concept of a singularity, where density becomes infinite, is a mathematical prediction and not a physical reality. Scientists believe that at the center of a black hole, there is a state of extreme density and curvature of spacetime, but it is not infinite.
Yes, there is a point called the event horizon, beyond which the gravitational pull of a black hole is too strong for anything, including light, to escape. However, objects that are far enough away from the black hole can still escape its gravitational pull.
No, black holes do not suck everything in like a vacuum. They have a strong gravitational pull, but they do not actively pull objects towards them. Instead, objects are pulled towards the black hole due to its immense mass and the curvature of spacetime around it.
Currently, scientists do not have enough evidence to support the idea that black holes can die or disappear. However, some theories suggest that they can evaporate over time through a process called Hawking radiation, but this process is very slow and would take trillions of years for a black hole to significantly shrink in size.