Kerr spacetime admits no conformally flat slicing of the form t = F(r, θ, a), with the obstruction appearing at fifth order in spin, and Kerr-de Sitter admits no analytic spatially flat slicing beyond linear order.
Black holes and stars in the minimal theory of massive gravity
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abstract
In this letter, we show that any solution of general relativity (GR) that can be rendered spatially flat by a coordinate change is also a solution of the self-accelerating branch of the minimal theory of massive gravity (MTMG), with or without matter. We then for the first time obtain black hole and star solutions in a theory of massive gravity that agree with the corresponding solutions in GR and that are free from strong coupling issues. This in particular implies that the parametrized post-Newtonian parameters $\beta^{\rm PPN}$ and $\gamma^{\rm PPN}$ are unity, as in GR. We further show how these solutions can be embedded in a cosmological setting. While cosmological scales have already been considered in previous works, this is the first study of the phenomenology at shorter scales of the self-accelerating branch of MTMG.
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On the absence of conformally flat slicings of the Kerr spacetime
Kerr spacetime admits no conformally flat slicing of the form t = F(r, θ, a), with the obstruction appearing at fifth order in spin, and Kerr-de Sitter admits no analytic spatially flat slicing beyond linear order.