The Komar mass function in the de-Rham-Gabadadze-Tolley non-linear theory of massive gravity

Abstract

I derive the Komar mass/function for the Schwarszchild de-Sitter (S-dS) black-hole inside the dRGT non-linear theory of massive gravity by taking the usual notion of time-like Killing vector in unitary gauge. The dRGT Komar function depends on the dynamics of the Stückelberg fields through the gauge transformation function. It goes to the standard value obtained in General Relativity (GR) 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 GR.

Version to appear in Physical Review D

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• Dark matter halos modeled by polytropic spheres influenced by the relict cosmological constant and trapping polytropes forming supermassive black holes