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arXiv 2304.12935gr-qc
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Einstein-非线性电动力学-Dilaton理论中由均匀电场支撑的脏黑洞

Dirty black hole supported by a uniform electric field in Einstein-Nonlinear Electrodynamics-Dilaton theory

S. Habib Mazharimousavi

备注：
16 pages 6 figures, final copy with minor corrections in figures 5 and 6, published in EPJC
发表信息：
Eur. Phys. J. C (2023) 83:406
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AI总结：

本文在引力与非线性电动力学和Dilaton场耦合的框架下，提出由均匀电场和奇异Dilaton标量场支撑的精确脏黑洞解，发现其在特定参数下热稳定且潮汐力行为有别于Schwarzschild黑洞。

摘要：

在本研究中，我们在引力与非线性电动力学（NED）和Dilaton场最小耦合的背景下，提出了一个精确的脏/毛黑洞解。该NED模型在文献中被称为平方根（SR）模型，即$\mathcal{L}\sim \sqrt{-\mathcal{F}}$。该黑洞解由均匀径向电场和奇异Dilaton标量场支撑，其时空为非渐近平坦且具有奇异性，奇点位于其中心。通过适当的变换，可得到一个有趣的线元$ds^{2}=-\left( 1-\frac{2M}{ρ^{η^{2}}} \right) ρ^{2\left( η^{2}-1\right) }dτ^{2}+\left( 1-\frac{2M}{ ρ^{η^{2}}}\right) ^{-1}dρ^{2}+\varkappa ^{2}ρ^{2}dΩ^{2} $，该线元包含两个参数，即质量$M$和Dilaton参数$ η^{2}>1$（$\varkappa ^{2}=\frac{1}{η^{2}}$），可被简单地视为脏Schwarzschild黑洞。这是因为当$η^{2}\rightarrow 1$时，时空退化为Schwarzschild黑洞。我们表明，尽管上述时空的因果结构与Schwarzschild黑洞相似，但它在$η^{2}>2$时是热稳定的。此外，该黑洞的潮汐力行为与Schwarzschild黑洞相同，但其大小取决于$η^{2}$，且其最小值并不对应于$η^{2}=1$（Schwarzschild极限）。

英文摘要：

In this study, we present an exact dirty/hairy black hole solution in the context of gravity coupled minimally to a nonlinear electrodynamic (NED) and a Dilaton field. The NED model is known in the literature as the square-root (SR) model i.e., $\mathcal{L}\sim \sqrt{-\mathcal{F}}.$ The black hole solution which is supported by a uniform radial electric field and a singular Dilaton scalar field is non-asymptotically flat and singular with the singularity located at its center. An appropriate transformation results in an interesting line element $ds^{2}=-\left( 1-\frac{2M}{ρ^{η^{2}}} \right) ρ^{2\left( η^{2}-1\right) }dτ^{2}+\left( 1-\frac{2M}{ ρ^{η^{2}}}\right) ^{-1}dρ^{2}+\varkappa ^{2}ρ^{2}dΩ^{2} $ with two parameters - namely the mass $M$ and the Dilaton parameter $ η^{2}>1$ ($\varkappa ^{2}=\frac{1}{η^{2}}$) - which may be simply considered as the dirty Schwarzschild black hole. This is because with $η^{2}\rightarrow 1$ the spacetime reduces to the Schwarzschild black hole. We show that although the causal structure of the above spacetime is similar to the Schwarzschild black hole, it is thermally stable for $η^{2}>2$. Furthermore, the tidal force of this black hole behaves the same as a Schwarzschild black hole, however, its magnitude depends on $η^{2}$\ such that its minimum is not corresponding to $η^{2}=1$\ (Schwarzschild limit).

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