Essays/Tensor Experiments/TensorExperiments24

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... ADDENDUM ...

...

...

...

... an energy distribution in an inertial reference frame ...

GTE2400C.jpg

... use ...

... a connection for covariant differentiation ...

GTE2401C.jpg

... for conservation of energy ...

GTE2402D.jpg

... the torsion tensor ...

GTE2403C.jpg

... use ...

... a connection for covariant differentiation ...

GTE2404C.jpg

... derive the Riemann-Christoffel tensor ...

GTE2405D.jpg

... covariant derivative of the Riemann-Christoffel tensor ...

GTE2406D.jpg

... use the torsion tensor ...

GTE2407D.jpg

... Bianchi identity ...

GTE2408D.jpg

... the field tensor ...

GTE2409C.jpg

... Bianchi identity in Cartesian coordinates ...

GTE2410D.jpg

... use ...

... a connection for covariant differentiation ...

GTE2411C.jpg

... Maxwell's equation (2) in Cartesian coordinates ...

... (derived from the Bianchi identity in Cartesian coordinates) ...

GTE2412E.jpg

... Maxwell's equation (1) in Cartesian coordinates ...

... (derived from the Bianchi identity in Cartesian coordinates) ...

GTE2413E.jpg

... use ...

... a connection for covariant differentiation ...

GTE2414C.jpg

... geodesics (gravity) ...

GTE2415D.jpg

...

...

...

... NOTE 1 ...

... raising and lowering indexes on tensors in Cartesian coordinates ...

GTE2416C.jpg

...

... NOTE 2 ...

... (+/-) results from skew-symmetric quantities ...

GTE2417C.jpg

Download: File:LTE2400C.txt
Download: File:LTE2401C.txt
Download: File:LTE2402D.txt
Download: File:LTE2403C.txt
Download: File:LTE2404C.txt
Download: File:LTE2405D.txt
Download: File:LTE2406D.txt
Download: File:LTE2407D.txt
Download: File:LTE2408D.txt
Download: File:LTE2409C.txt
Download: File:LTE2410D.txt
Download: File:LTE2411C.txt
Download: File:LTE2412E.txt
Download: File:LTE2413E.txt
Download: File:LTE2414C.txt
Download: File:LTE2415D.txt
Download: File:LTE2416C.txt
Download: File:LTE2417C.txt