Uniqueness of Self-Similar Asymptotically Friedmann-Robertson-Walker Spacetime in Brans-Dicke theory

We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state $p=(γ-1)μ(1 \le γ<2)$, we show that there are no non-trivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.

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