The problem of reconstruction for static spherically-symmetric $4D$ metrics in scalar-Einstein-Gauss-Bonnet model
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2025
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| author | Ernazarov, K. K. Ivashchuk, V. D. |
| author_facet | Ernazarov, K. K. Ivashchuk, V. D. |
| contents | We consider the $4D$ gravitational model with a scalar field $φ$, Einstein and Gauss-Bonnet terms. The action of the model contains a potential term $U(φ)$, Gauss-Bonnet coupling function $f(φ)$ and a parameter $\varepsilon = \pm1 $, where $\varepsilon = 1$ corresponds to ordinary scalar field and $\varepsilon = -1 $ - to phantom one. Inspired by the recent works of Nojiri and Nashed, we explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdal parametrization: $ds^2 = \left(A(u)\right)^{-1}du^2 - A(u)dt^2 + C(u)dΩ^2$, with given $A(u) > 0$ and $C(u) > 0$. The procedure gives the relations for $U(φ(u))$, $f(φ(u))$ and $dφ/du$, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a second order linear differential equation for the function $f(φ(u))$. The formalism is illustrated by two examples when: a) the Schwarzschild metric and b) the Ellis wormhole metric, are chosen as a starting point. For the first case a) the black hole solution with a ``trapped ghost'' is found which describes an ordinary scalar field outside the photon sphere and phantom scalar field inside the photon sphere. For the second case b) the sEGB-extension of the Ellis wormhole solution is found when the coupling function reads: $f(φ) = c_1 + c_0 ( \tan ( φ) + \frac{1}{3} (\tan ( φ))^3)$, where $c_1$ and $c_0$ are constants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The problem of reconstruction for static spherically-symmetric $4D$ metrics in scalar-Einstein-Gauss-Bonnet model Ernazarov, K. K. Ivashchuk, V. D. General Relativity and Quantum Cosmology High Energy Physics - Theory We consider the $4D$ gravitational model with a scalar field $φ$, Einstein and Gauss-Bonnet terms. The action of the model contains a potential term $U(φ)$, Gauss-Bonnet coupling function $f(φ)$ and a parameter $\varepsilon = \pm1 $, where $\varepsilon = 1$ corresponds to ordinary scalar field and $\varepsilon = -1 $ - to phantom one. Inspired by the recent works of Nojiri and Nashed, we explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdal parametrization: $ds^2 = \left(A(u)\right)^{-1}du^2 - A(u)dt^2 + C(u)dΩ^2$, with given $A(u) > 0$ and $C(u) > 0$. The procedure gives the relations for $U(φ(u))$, $f(φ(u))$ and $dφ/du$, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a second order linear differential equation for the function $f(φ(u))$. The formalism is illustrated by two examples when: a) the Schwarzschild metric and b) the Ellis wormhole metric, are chosen as a starting point. For the first case a) the black hole solution with a ``trapped ghost'' is found which describes an ordinary scalar field outside the photon sphere and phantom scalar field inside the photon sphere. For the second case b) the sEGB-extension of the Ellis wormhole solution is found when the coupling function reads: $f(φ) = c_1 + c_0 ( \tan ( φ) + \frac{1}{3} (\tan ( φ))^3)$, where $c_1$ and $c_0$ are constants. |
| title | The problem of reconstruction for static spherically-symmetric $4D$ metrics in scalar-Einstein-Gauss-Bonnet model |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.00244 |