Recent content by AEM

I have come to this thread rather late, however I'd like to make a few comments. Vector analysis was worked out in the early 1880s by the American mathematical physicist, J. Willard Gibbs. In the period 1881-1884, he circulated a pamphlet he had written to interested people and in 1901 Yale...

One of the easiest metrics to begin with is the spherically symmetric metric that leads to the Schwarzschild solution. Another relatively easy metric, but not quite as easy algebraically is the axi-symmetric metric that leads to the Weyl solution. As the previous post indicates, using computer...

Isn't there a problem with the indices here, or am I missing something? Three k's and 3 i's in each term doesn't ring true to me.

George, In your first post you mentioned the "Schwarzschild Constant Density Spherical Solution". Is this an "interior" solution? Could you cite a reference for it? Are there any interesting solutions interior to a spherical distribution of "dust" --this could not be static and would have to...

Thank you, Steve and George.

Thanks to all for the references on frame dragging. I have another question. Consider the very massive black holes believed to be at the center of most spiral galaxies. If they were rotating rapidly would the frame dragging effect alter the orbital dynamics of stars in orbit around the black hole?

Stevebd1, do you have a good reference for the derivation of the equations that describe frame dragging? Is this the same as the Lense-Thirring effect?

Here's how it works in detail: Each path that the girls takes can be represented by a vector. When drawn out in an x-y coordinate system you can express each vector in terms of its x and y components. The resultant vector is found by adding up all of the x components and then adding up all the y...

That is the correct approach. The resulting displacement is just the sum of those individual vectors. If you drew them to scale, you can connect the starting point to the ending point and measure that vector to get your answer.

Here are a couple of hints: (1) The time frame for the velocity and the acceleration is the same: 5 sec. (2) Find the distance that the tip of the second hand travels in 5 sec. You can do this by knowing that it travels 360 degrees, or 2 Pi radians in 60 seconds. From that tells you can figure...

Yes, you calculate each potential separately and then add them all up. For the curved pieces construct an integral for a potential dV from a bit of charge dq. then integrate. Your limits of integration depend on how you choose to draw your diagram, but the total angle is the same no matter how...

Several of your answers above are wrong. Why don't you check the following terms on Wikipedia: Refraction Diffraction Dispersion Finally, in an old film style camera the image is made by a chemical reaction. What is the difference between a real and a virtual image? Which one can induce...

Besides the approach that I mentioned in my previous post, you can also use the fact that Work = qV where q is the charge that's being moved, and V is the change in electric potential. What you calculated in your work below, was the change in electric potential, not the work. All you have to...

Also, I should mention that you are correct. Work is done only when the charged is moved along a radial path.

In brief, Work = Force times distance. So your equation for work should be W_{\vec{E}} = -\int_{r_{1}}^{r_{2}} q \vec{E}\cdot d\vec{r} Where the force is qE, q being the charge that's moved, and E is the field due to the charge Q.