Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model

Abstract

We consider the sEGB $4d$ gravitational model with a scalar field $\phi \left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(\phi \right)$, a Gauss-Bonnet coupling function $f\left(\phi \right)$ and a parameter $\epsilon =\pm 1$, where $\epsilon =1$ corresponds to the usual scalar field, and $\epsilon =-1$ to the phantom field. In this paper, the sEGB reconstruction procedure considered in our previous paper is applied to the metric of the Ellis-Bronnikov solution, which describes a massive wormhole in the model with a phantom field (and zero potential). For this metric, written in the Buchdal parameterization with a radial variable $u$, we find a solution of the master equation for $f\left(\phi \left(u\right)\right)$ with the integration (reconstruction) parameter $C_0$. We also find expressions for $U\left(\phi \left(u\right)\right)$ and $\epsilon {\dot{\phi }}^2=h\left(u\right)$ for $\epsilon =\pm 1$. We prove that for all non-trivial values of the parameter $C_0\ne 0$ the function $h\left(u\right)$ is not of constant sign for all admissible $u\in \left(-\infty ,+\infty \right)$. This means that for a fixed value of the parameter $\epsilon =\pm 1$ there is no non-trivial sEGB reconstruction in which the scalar field is a purely ordinary field ($\epsilon =1$) or a purely phantom field ($\epsilon =-1$).

17 pages, 2 figures, Latex, final version: 4 pages are added

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Cited by in corpus (1)

• The Yilmaz-Rosen and Janis-Newman-Winicour metric solutions in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model