- #1
Atticuskirk
- 2
- 0
And if so, how much? Should the radius be thought of as zero, an infinitesimal, or as the Planck length?
v2/r = ω2r
If its zero, then you immediately run into a problem when trying to calculate it with linear velocity.
v2/r = ar
v2/0 = undefined
OR
ω2r = ar
ω20 = 0
Which would mean that v2/r ≠ ω2r
If its an infinitesimal, then there's still a problem.
Let ε = 1/∞
v2/r = ar
v2/ε = ∞
ω2r = ar
ω2 = ε
v2/r = ω2r
∞=ε
The last case of r being equal to the Planck length seems to be the only one that makes sense, since its still a real number (just really, really tiny). So does this mean a black hole's singularity is not actually a mathematical singularity, or am I just misunderstanding something here?
v2/r = ω2r
If its zero, then you immediately run into a problem when trying to calculate it with linear velocity.
v2/r = ar
v2/0 = undefined
OR
ω2r = ar
ω20 = 0
Which would mean that v2/r ≠ ω2r
If its an infinitesimal, then there's still a problem.
Let ε = 1/∞
v2/r = ar
v2/ε = ∞
ω2r = ar
ω2 = ε
v2/r = ω2r
∞=ε
The last case of r being equal to the Planck length seems to be the only one that makes sense, since its still a real number (just really, really tiny). So does this mean a black hole's singularity is not actually a mathematical singularity, or am I just misunderstanding something here?