Relativity 108a: Schwarzschild Metric - Derivation

0:00 Introduction to Schwarzschild metric
5:12 Spherical Coordinates Review
7:30 Schwarzschild Metric Assumptions
10:59 Connection Coefficient Calculation
17:24 Ricci Tensor Calculation
22:35 Solving for A(r) and B(r)
24:47 Solving for Schwarzschild Radius
28:56 Warning + Conclusion

[canyadigit]

Tears of joy. I entered here not knowing what a metric even was and now am learning how to derive the Schwartz child metric via differential geometry. Thanks Chris 👍

[tobiasbendix]

Hello Chris! I recently graduated high school, and your videos on general relativity played a crucial role. In Denmark, every high school student must complete a special study project (SRP) during their final year. The project has to be at least 15 to 20 pages long and research a self-selected topic. I chose to focus my project on "The Derivation of the Schwarzschild Metric and Black Holes" (my physics teacher thought it might be challenging but not impossible for me to tackle).

Thanks to your videos, I was able to grasp complex concepts and present them effectively in my project. During the oral exam, where I had to defend my written work, both examiners were thoroughly impressed and commented that it might be the best project they had ever seen. Many thanks to you and your invaluable videos, Chris!

And by the way, my physics teacher and I are now your biggest fans after watching your videos almost on loop the last few months :-)

[warfyaa]

This channel is simply one of the most valuable things I've ever found not just on Youtube, but on the whole holly internet,
And I literally mean it.

[Richard.Holmquist]

Chris, the clarity of your videos, and your don’t skip the hard stuff rigor, have not only made an understanding of the Einstein field equations accessible to a seriously curious high school senior and certainly to a similarly curious college undergraduate, but also you have shown them the mathematical tools needed to solve the equations rather than simply a magical formula at the end.

The only comparison I can think of are the Feynman lectures on physics.

If there were an equivalent Nobel or Fields prize for what you have done to demystify for young students (any age, really)the many hang points of just partial understanding so common in normal teaching, you deserve that prize.

[m_bm_a]

The best courses of GR I have ever seen !! Thank you !!

[lanimulrepus]

You've obviously put a heck-of-lot of thought, time, and energy into this fine video... Enjoyed it...

[brendank]

I understand it will be a lot of work for you, but covering the kerr metric in the future would be extremely helpful. There are little to no derivations i can find for that metric online and most GR lectures skip over the derivation and jump right into using it.

[srmxe]

This Mr. Schwarzschild figured out Einstein's method in a couple months? Sitting in a trench with bullets overhead?? What a man! As are you Chris, thanks

[greenguo]

Thanks Chris. I was looking at Schwarzschild metric derivation yesterday and the only thing I could find was a 3-part series after watching which I was more confused. Chris to the save today! Thank you again and Google for keeping tabs of what I saw.

[gdmsave]

There is a typo on timestamp 15:50 and corresponding slide #54 from the presentation. In the bottom line g22 is non-zero. Thank you for wonderful lecture!

[demostheneslocke]

Btw if you want to make your matrices look better you can just add in blank rows to fix the non aligning issue

[KuhWristChin]

its amazing how we can freely access this level of information

[nikolaalfredi]

I am very excited for the new journey, I have always looked forward to it. I also have completed all of the Tensor series and as well as general relativity series... Now I will go beyond it. Thanks for uploading this video.

[steffenleo]

Happy New Year 2023 Chris. All the Best for you and your family. Thanks a lot for all the videos you make to cover tensoralgebra and cosmology...👍👍🙏

[monsurrahman]

Thank you, I have been waiting for your video

[chimetimepaprika]

nice presentation, dude. I gotta watch this a few more times.

[chintanpatel]

I was looking for this specific topic form you 😁😁😁 thanks I really have learned a lot from your Channel 😊

[jigold]

Thank You so very much for sharing and posting.

[vorperian_courses]

Excellent presentations and explanations. Really appreciate it. Thank you.

[soroushzare]

Thank you for the great work you did. It is possible to make a video about extracting torsion from metrics (the line element) that describe the topological defect space-time. For example, the extracting torsion from the line element describes a kind of dislocation in space-time.