Density of a Black Hole

aise0603

Mass falling into a black hole will approach the center of the black hole at a given velocity. As it approaches the center of the black hole, from our reference frame, there is time dialation. In fact, at some given closeness, a unit of planck time, in the mass's reference frame, is longer than the age of the universe.

Gravitational time dialation outside a non-rotating sphere
to = tf(1-2GM/(rc2))1/2

if to = planck time
tf = the age of the universe
r = planck distance

solve for M to find the smallest amount of mass that could possibly create a black hole

Ms = 1.09 X 10-8 kg

Density = Ms/Vs = 6.15718 X 1095kg/m3

Is that the most dense that anything could be in the universe?

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Dmitry67

What you have calculated is so called Planck Density:
http://en.wikipedia.org/wiki/Planck_units

It means that at such density we can't use GR or QM as is
We need to use more advanced theory which does not exist yet.

aise0603

But could it be that in a given reference frame, nothing can be more dense than this? Just like nothing can travel faster than the speed of light, in a given reference frame.

JustinLevy

As Dmitry mentioned, we have good reason to expect our current theories won't match nature very well in these regimes. And we definitely don't have experimental data from these regimes either. So no "real" answer can be given right now.

But if you are just asking what classical theory like GR says, then the answer is no: there is no density limit. Density is coordinate system dependent, so we can choose a coordinate system which makes it arbitrarily large if we wish. So there is no classical limit on density.

Even ignoring the coordinate system issues, what would you consider a point particle. For example, what is the density of an electron?

aise0603

As Dmitry mentioned, we have good reason to expect our current theories won't match nature very well in these regimes. And we definitely don't have experimental data from these regimes either. So no "real" answer can be given right now.

But if you are just asking what classical theory like GR says, then the answer is no: there is no density limit. Density is coordinate system dependent, so we can choose a coordinate system which makes it arbitrarily large if we wish. So there is no classical limit on density.

Even ignoring the coordinate system issues, what would you consider a point particle. For example, what is the density of an electron?
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