Tensor calculus | Tensor calculus for general relativity | Metric tensor | Cylindrical coordinates – YouTube

Tensor calculus | Tensor calculus for general relativity | Metric tensor | Cylindrical coordinates



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  • Video Views: 1920
  • Published On: 2022-02-06 18:34:53
  • Video Published/Author: Physics for Students- Unleash your power!!
  • Video Duration: 00:43:18
  • Source: Watch on YouTube


#tensorcalculus #tensorcalculusforgeneralrelativity #metrictensor

This video is about metric tensors. I have covered metric tensors of general relativity and how to find the metric tensor of cylindrical coordinates. I have also discussed in length covariant and contravariant tensors of rank 1 and rank 2 as well as the invariance and the symmetric nature of tensors. The law of transformation of tensors has also been discussed. Finally, I have discussed the various components of Einstein’s field equations, Ricci tensor, Ricci scalar, stress energy-momentum tensor as well as gravitational potential.

00:00 – 01:47 – Introduction
01:48 – 07:50 – A quick recap (From the pervious video)
07:51 – 15:50 – What is a total differential?
15:51 – 21:42 – Law of transformation for tensors
21:43 – 21:52 – Tensor algebra, covariant and contravariant vectors (Rank 1)
21:53 – 26:19 – Tensor algebra, covariant and contravariant vectors (Rank 2)
26:20 – 33:25 – Metric tensor (Invariance and symmetry)
33:26 – 37:35 – Finding the metric tensor of cylindrical coordinates (Derivation)
37:36 – 41:51 – Einstein’s field equations & the components
41:51 – 43:16 – Conclusion

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3 comments
  1. When you truly understand Special Relativity you come to understand that it is simply General Relativity after all, Einstein was wrong about acceleration, G≠a it is the energy input to the clock and the region of the fabric that the clock moves through that dictates the measurement of time. Plus as I show, we still have time at the speed of light and variable speeds of detected time at that.
    https://youtu.be/8L-t8Si5ka8

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