The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model
Abstract We consider the 4D gravitational model with a scalar field $$\varphi $$ φ , Einstein and Gauss–Bonnet terms. The action of the model contains a potential term $$U(\varphi )$$ U ( φ ) , Gauss–Bonnet coupling function $$f(\varphi )$$ f ( φ ) and a parameter $$\varepsilon = \pm 1 $$ ε = ± 1 ,...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14481-7 |
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| author | K. K. Ernazarov V. D. Ivashchuk |
| author_facet | K. K. Ernazarov V. D. Ivashchuk |
| author_sort | K. K. Ernazarov |
| collection | DOAJ |
| description | Abstract We consider the 4D gravitational model with a scalar field $$\varphi $$ φ , Einstein and Gauss–Bonnet terms. The action of the model contains a potential term $$U(\varphi )$$ U ( φ ) , Gauss–Bonnet coupling function $$f(\varphi )$$ f ( φ ) and a parameter $$\varepsilon = \pm 1 $$ ε = ± 1 , where $$\varepsilon = 1$$ ε = 1 corresponds to ordinary scalar field and $$\varepsilon = -1 $$ ε = - 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: $$ds^2 = \left( A(u)\right) ^{-1}du^2 - A(u)dt^2 + C(u)d\Omega ^2$$ d s 2 = A ( u ) - 1 d u 2 - A ( u ) d t 2 + C ( u ) d Ω 2 , with given $$A(u) > 0$$ A ( u ) > 0 and $$C(u) > 0$$ C ( u ) > 0 . The procedure gives the relations for $$U(\varphi (u))$$ U ( φ ( u ) ) , $$f(\varphi (u))$$ f ( φ ( u ) ) and $$d\varphi /du$$ d φ / d u , 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 $$f(\varphi (u))$$ 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: $$f(\varphi ) = c_1 + c_0 ( \tan ( \varphi ) + \frac{1}{3} (\tan ( \varphi ))^3)$$ f ( φ ) = c 1 + c 0 ( tan ( φ ) + 1 3 ( tan ( φ ) ) 3 ) , where $$c_1$$ c 1 and $$c_0$$ c 0 are constants. |
| format | Article |
| id | doaj-art-ea565e4349fb4ae3acd0b9ba8c8c91f1 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-ea565e4349fb4ae3acd0b9ba8c8c91f12025-08-20T03:46:13ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-07-0185711210.1140/epjc/s10052-025-14481-7The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet modelK. K. Ernazarov0V. D. Ivashchuk1Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University)Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University)Abstract We consider the 4D gravitational model with a scalar field $$\varphi $$ φ , Einstein and Gauss–Bonnet terms. The action of the model contains a potential term $$U(\varphi )$$ U ( φ ) , Gauss–Bonnet coupling function $$f(\varphi )$$ f ( φ ) and a parameter $$\varepsilon = \pm 1 $$ ε = ± 1 , where $$\varepsilon = 1$$ ε = 1 corresponds to ordinary scalar field and $$\varepsilon = -1 $$ ε = - 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: $$ds^2 = \left( A(u)\right) ^{-1}du^2 - A(u)dt^2 + C(u)d\Omega ^2$$ d s 2 = A ( u ) - 1 d u 2 - A ( u ) d t 2 + C ( u ) d Ω 2 , with given $$A(u) > 0$$ A ( u ) > 0 and $$C(u) > 0$$ C ( u ) > 0 . The procedure gives the relations for $$U(\varphi (u))$$ U ( φ ( u ) ) , $$f(\varphi (u))$$ f ( φ ( u ) ) and $$d\varphi /du$$ d φ / d u , 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 $$f(\varphi (u))$$ 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: $$f(\varphi ) = c_1 + c_0 ( \tan ( \varphi ) + \frac{1}{3} (\tan ( \varphi ))^3)$$ f ( φ ) = c 1 + c 0 ( tan ( φ ) + 1 3 ( tan ( φ ) ) 3 ) , where $$c_1$$ c 1 and $$c_0$$ c 0 are constants.https://doi.org/10.1140/epjc/s10052-025-14481-7 |
| spellingShingle | K. K. Ernazarov V. D. Ivashchuk The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model European Physical Journal C: Particles and Fields |
| title | The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model |
| title_full | The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model |
| title_fullStr | The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model |
| title_full_unstemmed | The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model |
| title_short | The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model |
| title_sort | problem of reconstruction for static spherically symmetric 4d metrics in scalar einstein gauss bonnet model |
| url | https://doi.org/10.1140/epjc/s10052-025-14481-7 |
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