Generalized Ellis-Bronnikov Wormhole Solution in the scalar-Einstein-Gauss-Bonnet 4d Gravitational Model

We consider the sEGB 4d gravitational model with a scalar field, Einstein and Gauss-Bonnet terms. The model action contains a potential term, a Gauss-Bonnet coupling function and a parameter, where corresponds to the usual scalar field, and 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 with the integration (reconstruction) parameter. We also find expressions for and for. We prove that for all non-trivial values of the parameter the function is not of constant sign for all admissible. This means that for a fixed value of the parameter there is no non-trivial sEGB reconstruction in which the scalar field is a purely ordinary field () or a purely phantom field (). © 2025 Elsevier B.V., All rights reserved.