I Multivariable Calculus Project: Spacetime/Black Holes

[pmrotman]

I am a student currently taking both Multivariable Calculus and Differential Equations. Instead of a final exam my teacher assigned a final project for Multivariable, and I chose to do something with Spacetime/Black holes. Within the scope of <100 hours of work, is there anything I can do with my current knowledge? At the moment I feel a bit overwhelmed with trying to learn Tensor calc.

 

[Nugatory]

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.

 

[pervect]

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.

 

[pmrotman]

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.

Thanks I'll check it out.

 

[pmrotman]

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.

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?

 

[Nugatory]

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?

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.

Black holes are somewhat irresistibly fascinating, but it will be hard to do them justice unless you're going to take on the mathematical preliminaries. But if you're feeling overwhelmed by tensor methods... Have you seen https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf ? Its section on tensors is no substitute for a serious differential geometry course, but it is very approachable and will give you enough background to get through a lot of neat stuff.

 

[robphy]

Project ideas in special relativity:

Show how the electromagnetic field and the Maxwell Equations (a set of multivariable partial differential equations) transform under a Lorentz transformation. Start with fields, then later start with the potentials.

Study the relativistic particle... Action, Lagrangian, Hamiltonian... Then, the charged relativistic particle...