How to calculate de d'Alembertian of a rank-2 antisymmetric tensor given by

$$ \Box T_{\mu\nu}=g^{\alpha\beta}\nabla_{\alpha}\nabla_{\beta}T_{\mu\nu} $$

while trying to simplify the result expression?

  • 3
    $\begingroup$ In what way do you want to simplify this? This is already as simple as it gets. $\endgroup$
    – Prahar
    Jul 21 at 15:19
  • $\begingroup$ @Prahar I mean like after doing the expansion $\endgroup$
    – Syn1110
    Jul 21 at 16:48
  • $\begingroup$ For what purpose? This is by far the simpler version of the formula. You need to give some context. Are you in the process of learning what these symbols mean or are you trying to solve some other problem of which this is a smaller part? $\endgroup$
    – Prahar
    Jul 21 at 18:47
  • $\begingroup$ Are you looking for the expansion in terms of partial derivatives in some coordinate system? Is the space curved or flat? $\endgroup$ Jul 21 at 19:49
  • $\begingroup$ I'm assuming you have a particular $T_{\mu\nu}$ in mind with this question, but seeing how we cannot read your mind, you might need to add some more details about the particular case you are interested in into this question. $\endgroup$
    – Kyle Kanos
    Jul 21 at 21:20