The discussion centers around a student's final project for Multivariable Calculus, focusing on spacetime and black holes. Participants explore potential project ideas and resources that align with the student's current knowledge and time constraints.
Participants generally agree on the importance of understanding special relativity and suggest various project ideas, but there is no consensus on a single approach or topic for the project. The discussion remains open-ended with multiple competing views on how to proceed.
Participants express varying levels of understanding regarding the mathematical prerequisites for discussing black holes and spacetime, indicating that the project scope may depend heavily on the student's comfort with advanced calculus and tensor methods.
Thanks I'll check it out.pervect said:You could try reading "Exploring black holes" by Taylor. It might not be hopelessly advanced, I think it has some workbooks/projects. I don't own it, unfortunately, though sample chapters are availble at the aurhtor's (E.F. Taylor) website.
Nugatory said:How much special relativity do you know? There's no shortage of interesting spacetime problems ieven in the flat spacetime of SR, before you get take on the much more demanding curved spacetime of general relativity and black holes.
How much classical mechanics and E&M do you know? Have you been through a calculus-based course on classical mechanics? You'll get better and more targeted answers if you can tell us more.
You said "Spacetime/Black holes" and there's a lot of spacetime that isn't black holes. Many introductory presentations of special relativity assume constant relative velocities (and instantaneous accelerations if changes of direction are required, as in the twin paradox) because that simplifying assumption reduces the amount of calculus that is required. Thus, if you are feeling a bit overwhelmed by tensor methods but still want a chance to experiment with multi-variable calculus and differential equations, you might look for special relativity problems that naturally involve accelerations: Born rigid motion, Bell's spaceship paradox, Rindler coordinates, the relativistic rocket equation come to mind.pmrotman said:I have a very limited understanding of E&M, but some understanding of Classical Mechanics. I do understand special relativity and some of general relativity, and I'm fairly good at teaching myself new things within a reasonable scope (e.g. simple calc-based mechanics). The project doesn't need to be particularly advanced as it will be presented to other students of my caliber, but this is my area of interest and I would enjoy doing a lot of work for it. Any other questions?