On a reconstruction procedure for special spherically symmetric metrics in the scalar-Einstein-Gauss-Bonnet model: the Schwarzschild metric test
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arXiv
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| Format: | Preprint |
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2024
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| author | Ernazarov, K. K. Ivashchuk, V. D. |
| author_facet | Ernazarov, K. K. Ivashchuk, V. D. |
| contents | The 4D gravitational model with a real scalar field $φ$, Einstein and Gauss-Bonnet terms is considered. The action contains the potential $U(φ)$ and the Gauss-Bonnet coupling function $f(φ)$. For a special static spherically symmetric metric $ds^2 = (A(u))^{-1} du^2 - A(u) dt^2 + u^2 dΩ^2$, with $A(u) > 0$ ($u > 0$ is a radial coordinate), we verify the so-called reconstruction procedure suggested by Nojiri and Nashed. This procedure presents certain implicit relations for $U(φ)$ and $f(φ)$ which lead to exact solutions to the equations of motion for a given metric governed by $A(u)$. We confirm that all relations in the approach of Nojiri and Nashed for $f(φ(u))$ and $φ(u)$ are correct, but the relation for $U(φ(u))$ contains a typo which is eliminated in this paper. Here we apply the procedure to the (external) Schwarzschild metric with the gravitational radius $2 μ$ and $u > 2 μ$. Using the ``no-ghost'' restriction (i.e., reality of $φ(u)$), we find two families of $(U(φ), f(φ))$. The first one gives us the Schwarzschild metric defined for $u > 3 μ$, while the second one describes the Schwarzschild metric defined for $2 μ< u < 3 μ$ ($3 μ$ is the radius of the photon sphere). In both cases the potential $U(φ)$ is negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a reconstruction procedure for special spherically symmetric metrics in the scalar-Einstein-Gauss-Bonnet model: the Schwarzschild metric test Ernazarov, K. K. Ivashchuk, V. D. General Relativity and Quantum Cosmology High Energy Physics - Theory The 4D gravitational model with a real scalar field $φ$, Einstein and Gauss-Bonnet terms is considered. The action contains the potential $U(φ)$ and the Gauss-Bonnet coupling function $f(φ)$. For a special static spherically symmetric metric $ds^2 = (A(u))^{-1} du^2 - A(u) dt^2 + u^2 dΩ^2$, with $A(u) > 0$ ($u > 0$ is a radial coordinate), we verify the so-called reconstruction procedure suggested by Nojiri and Nashed. This procedure presents certain implicit relations for $U(φ)$ and $f(φ)$ which lead to exact solutions to the equations of motion for a given metric governed by $A(u)$. We confirm that all relations in the approach of Nojiri and Nashed for $f(φ(u))$ and $φ(u)$ are correct, but the relation for $U(φ(u))$ contains a typo which is eliminated in this paper. Here we apply the procedure to the (external) Schwarzschild metric with the gravitational radius $2 μ$ and $u > 2 μ$. Using the ``no-ghost'' restriction (i.e., reality of $φ(u)$), we find two families of $(U(φ), f(φ))$. The first one gives us the Schwarzschild metric defined for $u > 3 μ$, while the second one describes the Schwarzschild metric defined for $2 μ< u < 3 μ$ ($3 μ$ is the radius of the photon sphere). In both cases the potential $U(φ)$ is negative. |
| title | On a reconstruction procedure for special spherically symmetric metrics in the scalar-Einstein-Gauss-Bonnet model: the Schwarzschild metric test |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.01301 |