Abstract
We obtain two dimensional analogue of the Jordan-Brans-Dicke (JBD) gravity action described in four dimensional spherically symmetric curved space time metric. There will be two scalar fields, namely, the Brans Dicke (BD) ϕ and scale factor of 2-sphere part of the space time ψ. We obtained suitable duality transformations between (ψ, ϕ) and (ρ, S) where ρ and S is respectively amplitude and phase part of the corresponding de Broglie pilot wave function \(\Psi (\rho ,S)=\sqrt {\rho }e^{iS}.\) Covariant conservation of mass-energy current density of particles ensemble J a = ρ∂ a S, is established by applying a particular dynamical conformal frame described by (ρ, S).
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Ghaffarnejad, H. Spherically Symmetric Jordan-Brans-Dicke Quantum Gravity with de Broglie Bohm Pilot Wave Perspective. Int J Theor Phys 53, 2616–2622 (2014). https://doi.org/10.1007/s10773-014-2059-z
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DOI: https://doi.org/10.1007/s10773-014-2059-z