General form of the function $f(\mathbb{Q})$ using cylindrically static spacetime
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929742680162304 |
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| author | Nashed, G. G. L. |
| author_facet | Nashed, G. G. L. |
| contents | We find an exact static solution in four dimensions to the field equations of the $f(\mathbb{Q})$ gravity by using a cylindrically static spacetime with two different ansatz, $ν(r)$ and $μ(r)$. This solution is derived without imposing any conditions on $f(\mathbb{Q})$. The black hole solution involves four constants: $c_1$, $c_2$, $c_3$, and $c_4$. Among these, $c_1$ is linked to the cosmological constant, $c_2$ to the black hole's mass, while $c_3$ and $c_4$ are responsible for the deviation of the solution from the linear form of $f(\mathbb{Q})$. We demonstrate how the analytical function $f(\mathbb{Q})$ relies on $c_3$. When $c_3$ is zero, $f(\mathbb{Q})$ becomes a constant function, leading to the non-metricity case. We investigate the singularity of this solution and show that the Kretschmann invariant has a much milder singularity compared to the non-metricity case. We produce a black hole that rotates with non-vanishing values of $\mathbb{Q}$ and $f(\mathbb{Q})$ by using a coordinate transformation. Then, we analyze the laws of thermodynamics to determine the physical characteristics of this black hole solution and demonstrate that it is locally thermodynamically stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General form of the function $f(\mathbb{Q})$ using cylindrically static spacetime Nashed, G. G. L. General Relativity and Quantum Cosmology High Energy Physics - Theory We find an exact static solution in four dimensions to the field equations of the $f(\mathbb{Q})$ gravity by using a cylindrically static spacetime with two different ansatz, $ν(r)$ and $μ(r)$. This solution is derived without imposing any conditions on $f(\mathbb{Q})$. The black hole solution involves four constants: $c_1$, $c_2$, $c_3$, and $c_4$. Among these, $c_1$ is linked to the cosmological constant, $c_2$ to the black hole's mass, while $c_3$ and $c_4$ are responsible for the deviation of the solution from the linear form of $f(\mathbb{Q})$. We demonstrate how the analytical function $f(\mathbb{Q})$ relies on $c_3$. When $c_3$ is zero, $f(\mathbb{Q})$ becomes a constant function, leading to the non-metricity case. We investigate the singularity of this solution and show that the Kretschmann invariant has a much milder singularity compared to the non-metricity case. We produce a black hole that rotates with non-vanishing values of $\mathbb{Q}$ and $f(\mathbb{Q})$ by using a coordinate transformation. Then, we analyze the laws of thermodynamics to determine the physical characteristics of this black hole solution and demonstrate that it is locally thermodynamically stable. |
| title | General form of the function $f(\mathbb{Q})$ using cylindrically static spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.02902 |