PAllen's latest activity

Also note that the constraint of constant density per a local, comoving observer, means adding particles to outer rings as they are sped...

I think I have the key notion for the finite to continuum transition that explains the counterintuitive continuum result. The uniform...

But the uniform COM frame density follows necessarily from any simple (i.e. not including stress energy of holding the disc together)...

I don’t think the improper integral is the issue at all. In some sense, you never need to get there. Intuition suggests that any chosen...

Note that if we change the mass assumption to be constant density in each element's local comoving frame, we get for an arbitrary...

To decouple an annulus from any hypothetical containing disc, we introduce ##\rho## which is simply ##M/\pi r^2## in post #1 convention...

This is a nice simplification for further discussion, that changes the main questions not at all. This would be computing the total...

If I am picking, for example, a finite set of approximating elements, I can certainly have the angular span of each be inversely...

I think this can be dispensed with. Just keep ##r d\phi## constant along a radial path. Also, @Ibix integral in the OP already keeps...

This would be the same as long as you have uniformly distributed rest mass per the COM inertial frame. To get any other result you have...

It’s possibly important to understand what M means. The construction of the integral means it summed from constituent rest masses.

I am simply describing a procedure to arrive at the final state starting from a rest state.

The proposed integral in the OP impies the following physical process: a disc of dust with uniform density in some inertial frame is...

I claim the integral in the OP, evaluated between specified r values below R corresponding to speed c, will always be finite, and no...

There is one more way to look at the problem, to avoid the continuum distribution of matter in the radial direction. Consider ##N##...