Recent content by diracs-cat

That makes sense to me. The Bonnor beam is infinite, so the distribution of energy and momentum within any finite-length "control volume" cylinder surrounding it would be constant over time. So that results in a static spacetime. I assume if the beam were instead finite then the spacetime could...

This is really great information, everyone! Below is a summary of my understanding of the above discussion and one clarifying question below. Apologies for any more mistakes. I'm very much still a beginner at GR. 1) The Bonnor beam's spacetime metric is non-stationary, which means that...

Thanks for the interesting discussions and feedback everybody! I'm not sure I understand why non-stationary spacetimes would have "no gravitational time dilation" rather than just having gravitational time-dilation that is time-varying (or perhaps not uniquely defined), but that's not quite my...

Background: The "Bonnor beam" is an exact solution to the Einstein Field Equations for an infinitely-long, thin cross-section of electromagnetic radiation. It is an example of a "p-p wave" solution of the EFEs. The interior metric solution is as follows, where m is the energy density of the...

That worked great, thanks!

Thanks! Do you happen to know if there's some way I can configure xAct to get it to simplify the expressions the way it did for you? My Lagrangian and field equations aren't looking exactly like yours for some reason. Here's what I got. Thanks again for all your support here!

Thanks for the quick reply! For a simple covariant Lagrangian, I would say the Maxwell Lagrangian in curved spacetime. Just to be clear I'm not interested in solving this Lagrangian in particular, but interested in finding a computer algebra software/package that can do this in general. Also if...

Does anybody know of a software (or software package) that can solve the Euler-Lagrange field equations for a manifestly-covariant Lagrangian density in full tensor form? Mathematica has a "Variational Methods" package, but none of the examples given are in manifestly-covariant form. I am not...