Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915621957009408 |
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| author | Ernazarov, K. K. |
| author_facet | Ernazarov, K. K. |
| contents | We consider the sEGB $4d$ gravitational model with a scalar field $φ\left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(φ\right)$, a Gauss-Bonnet coupling function $f\left(φ\right)$ 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(φ\left(u\right)\right)$ with the integration (reconstruction) parameter $C_0$. We also find expressions for $U\left(φ\left(u\right)\right)$ and $\varepsilon \dotφ^2 = h\left(u\right)$ 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 ($\varepsilon = - 1$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model Ernazarov, K. K. General Relativity and Quantum Cosmology We consider the sEGB $4d$ gravitational model with a scalar field $φ\left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(φ\right)$, a Gauss-Bonnet coupling function $f\left(φ\right)$ 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(φ\left(u\right)\right)$ with the integration (reconstruction) parameter $C_0$. We also find expressions for $U\left(φ\left(u\right)\right)$ and $\varepsilon \dotφ^2 = h\left(u\right)$ 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 ($\varepsilon = - 1$). |
| title | Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.06223 |