Recent content by DiamondGeezer

I think the point of the thought experiment was that the sand was supplied by a second co-moving truck traveling at v Thus for the truck, although it's mass is changing, there is no change of velocity. What happens if the truck is moving up a slope of \theta degrees? Does the truck gain or...

In one of my undergrad books on physics is the example of a rail truck of mass M on a frictionless railroad moving at a constant speed v, which is being filled with sand at a rate of x kg/s If force F is applied to the truck, then the truck does not accelerate because F=m \frac{dv}{dt} +...

I think the main reason for the lack of attention was that Gibbs published in an obscure journal in Connecticut, and most of his insights became clearer after other people had independently reproduced his results.

Unfortunately the volume of a Schwarzschild Black Hole is zero using Schwarzschild coordinates, infinite if using Kruskal Szekeres coordinates (but if you include the event horizon the volume is [zero times infinity] which could be anything). This makes calculating the density of a black hole...

Yes.

I'm not going to stretch this thread to infinity. I'd like to pick up one comment: No, I'll take that as read. The question remains as to why so many coordinate systems have been constructed. Unfortunately black holes are not coordinate invariant. They are a product of a bad choice...

There's a fundamental difference between the line integral of a geodesic and an "arbitrary parametrized path". Perhaps you should stop and think before making such an obvious mistake. The continuous line integral of a geodesic is always normal to the event horizon and there is no function which...

How do you draw a line inside the horizon? In order to do that, the line must be composed of real spacelike integrals of non-zero length. But there are no spacelike integrals at all. Once again you've moved from the continuous integral outside the EH to a different integral "inside" the EH by...

There are no spacelike paths inside the EH. Only timelike ones. But we're not in real spacetime below the event horizon. We're in imaginary spacetime.

Now think about that. How to measure the spacetime differentials between two events each outside the causal light cone of the other? Think...think...no its gone. So the coordinates are not imaginary (and who said that they were?) but the spacetime distance between them is imaginary. Well...

Ah, but DrGreg if there are two "disjoint" systems then there cannot be a continuous worldline that connects the infalling particle from the Universe to the singularity. But Kruskal-Szekeres has the same problem with the inner and outer integrals as I've pointed out. What K-S does is define...

Another "proof by assertion". If there is no space to be measured, there cannot be "spacial separation". Also, there are no geodesics to the "singularity" because at the event horizon, all line integrals are normal to the spatial direction.

At the event horizon (and below) there's no such thing as a spatial separation. All separations are (imaginary) and solely timelike - whatever that means.

Sweet Jeebus do I have to repeat myself again? U V = \left(1-\frac{r}{2GM}\right)e^{r/2GM} becomes negative when r<2GM, which means that for an infalling particle (d\Omega^2 =0) then the dU dV also becomes negative WHICH MEANS THAT THE SPACETIME SEPARATION BECOMES IMAGINARY BECAUSE ITS THE...

Except that you have claimed that the "signs of g_{rr} and g_{tt} are reversed" when r<2M, which is wrong. Both separations spacelike or timelike become imaginary when r<2M - they do not become the other, they become something else entirely. That is the mathematical fudge which I have been...