Komar mass function in the de Rham-Gabadadze-Tolley nonlinear theory of massive gravity

I derive the Komar mass/function for the Schwarszchild-de Sitter black hole inside the de Rham-Gabadadze-Tolley nonlinear theory of massive gravity by taking the usual notion of timelike Killing vector in unitary gauge. The de Rham-Gabadadze-Tolley Komar function depends on the dynamics of the Stuckelberg fields through the gauge transformation function. It goes to the standard value obtained in general relativity if the spatial derivative of the gauge function vanishes. In such a case, the (gauge) function corresponds to the usual notion of time as in general relativity.