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

Source: [Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model](<https://www.sota2.com/research/paper/68fa49e01e209131ce93a4b0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-19T05:01:30.460Z

Authors: K. K. Ernazarov

Published: 2025-04-08T17:12:23.000Z

## Abstract

We consider the sEGB $4d$ gravitational model with a scalar field $\\varphi\\left(u\\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\\left(\\varphi\\right)$, a Gauss-Bonnet coupling function $f\\left(\\varphi\\right)$ and a parameter $\\varepsilon = \\pm 1$, where $\\varepsilon = 1$ corresponds to the usual scalar field, and $\\varepsilon = -1$ 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(\\varphi\\left(u\\right)\\right)$ with the integration (reconstruction) parameter $C\_0$. We also find expressions for $U\\left(\\varphi\\left(u\\right)\\right)$ and $\\varepsilon \\dot{\\varphi}^2 = h\\left(u\\right)$ for $\\varepsilon = \\pm 1$. We prove that for all non-trivial values of the parameter $C\_0 \\neq 0$ 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 $\\varepsilon = \\pm 1$ there is no non-trivial sEGB reconstruction in which the scalar field is a purely ordinary field ($\\varepsilon = 1$) or a purely phantom field ($\\varepsilon = - 1$).

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2504.06223>)

[PDF](<https://arxiv.org/pdf/2504.06223.pdf>)