http://arxiv.org/abs/2209.11011
It was shown a few years back that for the Brans-Dicke theory with a positive cosmological constant $\Lambda$, and a de Sitter or cosmological event horizon in the asymptotic region, not only there exist no non-trivial field configurations, but also the inverse Brans-Dicke parameter $\omega^{-1}$ must be vanishing, thereby essentially reducing the theory to Einstein’s General Relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $\phi$, couples directly to the $\Lambda$-term in the energy-momentum tensor as well as in its equation of motion, perhaps it is reasonable to ask : can $\phi$ become strong instead and screen the effect of $\Lambda$ at very large scales, so that the asymptotic de Sitter structure is replaced by some physically acceptable alternative non-singular boundary condition? In this work we analytically argue that under the assumption of any generic asymptotic stationary spacetime structure in the absence of a cosmological event horizon, similar non-existence results hold, as long as the spacetime is free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $\Lambda$, and for any generic asymptotic spacetime structure free from curvature singularity, a stationary black hole or even a star solution in the Brans-Dicke theory always necessitates $\omega^{-1}=0$, and thereby reducing the theory to General Relativity.
M. Ali, S. Bhattacharya and S. Kaushal
Fri, 23 Sep 22
17/70
Comments: v1; 10pp, 4 figs
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