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Gordon and Kerr-Schild ansatze in massive and bimetric gravity
We develop the "generalized Gordon ansatz" for the ghost-free versions of
both massive and bimetric gravity, an ansatz which is general enough to include
almost all spacetimes commonly considered to be physically interesting, and
restricted enough to greatly simplify calculations. The ansatz allows explicit
calculation of the matrix square root gamma = sqrt{g^{-1} f} appearing as a
central feature of the ghost-free analysis. In particular, this ansatz
automatically allows us to write the effective stress-energy tensor as that
corresponding to a perfect fluid. A qualitatively similar "generalized
Kerr-Schild ansatz" can also be easily considered, now leading to an effective
stress-energy tensor that corresponds to a null fluid. Cosmological
implications are considered, as are consequences for black hole physics.
Finally we have a few words to say concerning the null energy condition in the
framework provided by these ansatze.Comment: 22 page
Null Energy Condition violations in bimetric gravity
We consider the effective stress-energy tensors for the foreground and
background sectors in ghost-free bimetric gravity. By considering the
symmetries of the theory, we show that the foreground and background null
energy conditions (NECs) are strongly anti-correlated. In particular, the NECs
can only be simultaneously fulfilled when they saturate, corresponding to
foreground and background cosmological constants. In all other situations,
either the foreground or the background is subject to a NEC-violating
contribution to the total stress-energy.Comment: v1: 16 pages; v2: 2 references adde
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