Quick Notation Question

robousy

Hey, I'm going through Hawking and Ellis and want to confirm I have understood some notation correctly.

Are the following correct?

[tex]V_{(c;d)}=\nabla_c V^d + \nabla_d V^c[/tex]

and

[tex]V_{[c;d]}=\nabla_c V^d - \nabla_d V^c[/tex]

Also, do these have specific names?

Thanks in advance!!

Richard

robphy

[tex]V_{(c;d)}=\frac{1}{2!} \left( \nabla_d V_c + \nabla_c V_d \right)[/tex]

and

[tex]V_{[c;d]}=\frac{1}{2!}\left( \nabla_d V_c - \nabla_c V_d \right)[/tex]

The combinatorial factor is a convenient convention.
With it, you can call these the symmetric and antisymmetric parts of [tex]V_{c;d}[/tex].
You could call the antisymmetric part the "curl" of [tex]V_c[/tex].


Note that the operation
[tex]{(something)}_{;d}[/tex] is the same as [tex]\nabla_d (something)[/tex]

robousy

Ok Rob! Thanks a lot for clarifying that for me. Very much appreciated.