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Quick Notation Question

  1. Mar 5, 2008 #1
    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
     
    Last edited: Mar 5, 2008
  2. jcsd
  3. Mar 5, 2008 #2

    robphy

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    [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]
     
  4. Mar 5, 2008 #3
    Ok Rob! Thanks a lot for clarifying that for me. Very much appreciated.

    :smile:
     
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