2025/04/08 by Ernazarov, K. K. · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2504.06223
We consider the sEGB 4d gravitational model with a scalar field φ(u), Einstein and Gauss-Bonnet terms. The model action contains a potential term U(φ), a Gauss-Bonnet coupling function f(φ) and a parameter ε = ± 1, where ε = 1 corresponds to the usual scalar field, and ε = -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(φ(u)) with the integration (reconstruction) parameter C0. We also find expressions for U(φ(u)) and ε φ2 = h(u) for ε = ± 1. We prove that for all non-trivial values of the parameter C0 ≠ 0 the function h(u) is not of constant sign for all admissible u ∈ (-∞ , +∞). This means that for a fixed value of the parameter ε = ± 1 there is no non-trivial sEGB reconstruction in which the scalar field is a purely ordinary field (ε = 1) or a purely phantom field (ε = - 1).