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arXiv 2309.02452gr-qchep-th
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带电柱对称时空中 $f(T)$ 的一般表达式

The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions

G. G. L. Nashed

备注：
17 pages and four figures
发表信息：
Physics of the Dark Universe, Volume 42, December 2023, 101312
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AI总结：

本研究利用修正teleparallel等效广义相对论场方程，得到无约束n维静态带电黑洞精确解，分析其奇点、能量与热力学性质，并推导旋转解，发现黑洞在特定维度下无奇点且热稳定。

摘要：

利用修正的teleparallel等效广义相对论（记为 $\mathit{f(T)}$）的场方程，我们在不施加任何约束的情况下，得到了n维静态带电黑洞的精确解。该黑洞具有两个独特的维度常数：$m$ 和 $v$，其单位为{\textit 长度}。第一个常数与质量相关，而第二个常数代表电荷。这种电荷的存在使得黑洞偏离了teleparallel等效广义相对论（TEGR）的预期。我们的分析表明，$\mathit{f(T)}$ 依赖于参数 $v$，当 $v$ 被赋值为零时，它变成一个常数表达式。这个特定黑洞的一个引人入胜之处在于，当维度 $n$ 落在 $4 \leq n \leq 6$ 区间内且 $r$ 趋近于零时，由挠率和曲率构成的量不存在奇点。然而，对于 $n\geq7$，奇点比TEGR的情况更温和。此外，通过利用守恒的n-动量矢量，我们计算了这个解的能量，并确认其与ADM质量对应，精确到 $O\Big(\frac{1}{r}\Big)$ 阶。否则，我们观察到来自电荷项的高阶贡献。通过对黑洞应用坐标变换，我们推导出一个描述稳态旋转黑洞的精确解。该解展示了挠率标量和解析函数 $\mathit{f(T)}$ 的重要读数。为了深入了解这个黑洞的物理特性，我们计算了与热力学相关的各种物理量，如熵、霍金温度和热容量。分析表明，该黑洞表现出热稳定性。

英文摘要：

By utilizing the field equations of the modified teleparallel equivalent of general relativity, denoted as $\mathit{f(T)}$, we obtain an exact solution for a static charged black hole in n-dimensions, without imposing any constraints. The black hole possesses two distinctive dimensional constants: $m$ and $v$ with unit {\textit length}. The first constant is associated with the mass, while the second constant represents the electric charge. The existence of this electrical charge causes the black hole to diverge from the expectations of the teleparallel equivalent of general relativity (TEGR). Our analysis demonstrates that $\mathit{f(T)}$ is reliant on the parameter $v$ and transforms into a constant expression when $v$ is assigned a value of zero. A captivating aspect of this particular black hole is its absence of singularities in the quantities formed using torsion and curvature, given that the dimension $n$ falls within the interval of $4 \leq n \leq 6$ as $r$ approaches zero. However, for $n\geq7$, the singularity becomes milder in comparison to the case of TEGR. Furthermore, By utilizing the conserved n-momentum vector, we calculate the energy of this solution and confirm its correspondence with the ADM mass, accurate to the order of $O\Big(\frac{1}{r}\Big)$. Otherwise, we observe higher-order contributions arising from the electric charge terms. Through the application of a coordinate transformation to the black hole, we derive a precise solution describing a stationary rotating black hole. This solution showcases significant readings of the torsion scalar and the analytical function $\mathit{f(T)}$. In order to gain insight into the physics of this black hole, we calculate various physical quantities related to thermodynamics, such as entropy, Hawking temperature, and heat capacity. The analysis reveals that the black hole exhibits thermal stability.

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