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The k-essence theory with a power-law function of \((\partial \phi )^2\) and Rastall’s non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k–R duality) holds for static configurations with various symmetries ...

In this paper, we determine regular black hole solutions using a very general f(R) theory, coupled to a non-linear electromagnetic field given by a Lagrangian \(\mathcal {L}_\mathrm{NED}\). The functions f(R) and \(\mathcal {L}_\mathrm{NED}\) are in principle left unspecified. Instead, the model is constructed through a choice of the mass function M(r) presented in the metric ...

The Reduced Relativistic Gas (RRG) model was introduced by A. Sakharov in 1965 for deriving the cosmic microwave background (CMB) spectrum. It was recently reinvented by some of us to achieve an interpolation between the radiation and dust epochs in the evolution of the Universe. This model circumvents the complicated structure of the Boltzmann–Einstein system of equations and ...

We formulate a theory combining the principles of scalar–tensor gravity and Rastall’s proposal of a violation of the usual conservation laws. We obtain a scalar–tensor theory with two parameters \(\omega \) and \(\lambda \), the latter quantifying the violation of the usual conservation laws (\(\lambda = 1\) corresponding to the General Relativity limit). The only exact spherically ...