General form of the function $f(\mathbb{Q})$ using cylindrically static spacetime

Fuente: arXiv
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Main Author: Nashed, G. G. L.
Format: Preprint
Published: 2025
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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
id 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