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arXiv 2010.10312gr-qc
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Einstein-Maxwell-Gauss-Bonnet-Scalar理论中新的多毛黑洞解

Novel Hairy Black Hole Solutions in Einstein-Maxwell-Gauss-Bonnet-Scalar Theory

Callum L Hunter, Douglas J Smith

摘要:

以前已经证明,高斯-邦纳项非最小耦合到标量场产生标量化的黑洞解,它可以被认为是具有二级标量头发,参数化的黑洞的质量和电荷。在本文中,我们扩展了以前研究的线性耦合的形式$f(ϕ)=ϕ$的非最小耦合麦克斯韦项,与形式$\frac{1}{8}F_{μν}F^{μν}+βϕF_{μν}F^{μν}$。通过使用数值方法的解决方案,全微分方程,以及微扰展开的$r\rightarrow\infty$限制和微扰展开的耦合参数,如$β$。这些解描述了具有修正电场的标度化黑洞,修正电场不仅依赖于黑洞的电荷,还依赖于非最小耦合常数和黑洞的视界半径或质量.我们还讨论了解的实性条件对黑洞参数的影响,给出了一些明确的数值界。

英文摘要:

It has been previously shown that a Gauss-Bonnet term non-minimally coupled to a scalar field produces a scalarised black hole solution, which can be considered as having secondary scalar hair, parametrised in terms of the black hole's mass and charge. In this paper we extend a previously investigated linear coupling of the form $f(ϕ)=ϕ$ to a non-minimally coupled Maxwell term, with the form $\frac{1}{8}F_{μν}F^{μν}+βϕF_{μν}F^{μν}$. By using numerical methods the solutions to the full differential equations are found, as well as a perturbative expansion in the $r\rightarrow\infty$ limit and a perturbative expansion in couplings parameters such as $β$. These solutions describe scalarised black holes with modified electric field which have dependence not only on the electric charge of the black hole, but also the value of the non-minimal coupling constant and the horizon radius or mass of the black hole. We also discuss the bounds imposed on the parameters of the black hole by the reality condition of the solution, giving some explicit numerical bounds.

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