Tensors and Relativity: Chapter 8

The Ricci Tensor

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From the Riemann tensor:

equation1009

we obtain:

eqnarray1011

Unless tex2html_wrap_inline1239 or tex2html_wrap_inline1241 these components vanish. Also tex2html_wrap_inline1243 . Using the above expressions let us work out the non- zero components of the Ricci tensor tex2html_wrap_inline1245 . For example

eqnarray1013

so

eqnarray1015

This simplifies to

equation1017

The other components of the Ricci tensor are [ Assignment 7 ]:

eqnarray1019

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