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GR is what I'm working out of. Misner, Lewis, and plenty of YouTube lectures. It was simply a construct that I had imagined...

I'm just in my beginning stages of learning the theory. I've derived just about everything, but i don't understand the stress tensor, or how to construct it. I would like to be able to solve problems, and this is one that came to mind.

How would one go about setting up the stress energy tensor for a particle, say an electron subjected to electric an electric field that makes the particle oscillate with frequency \omega?

could you also prove why it's zero. Mathematically.

Okay, let us change the problem to a spinning problem too.

Suppose two masses are connected via a really strong spring, where one of the masses undergo an acceleration towards a relativistic speed, by say a rocket that leaves the scene soon after. When in isolation, (the two masses), they exhibit a sinusoidal oscillation to and fro. What is the...

What if perhaps we had a mechanism that made it such that the mass oscillates with constant /omega

Let a mass oscillate with relativistic acceleration (sinusoidal) by means which are irrelevant. What does the gravitational field look like a distance R away?

thank you :)

I thought it to be implied that proof, and or derivation of any of the mathematical constructs involved, and for that, I apologize.

Hi, I wish to not only learn, but prove every theory I come across. This requires a ton of math research, and at this point, I am about to begin quantum mechanics, and general relativity after I finish up my differential geometry book. My question, I suppose, is after I finish differential...

What would be better?

I believe this to be the way to approach. Then the evaluation of the new integral is straightforward. <Mod note: attachment deleted>

Hope this helps someone!

Hope this derivation helps someone!

The Lorentz equations are contingent upon the postulates. Without them, there are no equations.

My derivation of Taylor expansion. Hope someone struggling with it gets use!

Any advice on my derivation layout?

You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).

I know so little about the tiny world that provides us our laws. I am under the assumption that particles oscillate in general. I just want to know how. Not why. The why is easy.

How do protons oscillate? Do they move back and forth with a constant velocity, or sort of like a mass on a spring? If so, what is the frequency of oscillation? Thanks

Thank you for the response.

Thank you for the response. I was just confused because I assumed a luminiferous ether.

Both the Newtonian theory on gravitation and the General theory of Relativity predict a change in the direction of a beam of light as it propagates past a large mass. Regardless of the precision of the Δ velocity component (the component that can represent the vertical shift towards a mass), If...