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arXiv 2212.07296hep-thgr-qc
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$R^{2}$对黑弦不稳定性和增强黑弦的修正

$R^{2}$ corrections to the black string instability and the boosted black string

Carla Henríquez-Báez, Julio Oliva, Marcelo Oyarzo, Marcel I. Yáñez Reyes

摘要:

我们考虑了一个微扰Gauss-Bonnet项补充Einstein-Hilbert作用量,并计算了它对五维广义相对论中黑弦的Gregory-Laflamme不稳定性的标量模谱的影响.在研究了静态黑弦的一些性质后,我们给出了Lichnerowicz算子在$\mathcal{O}(α^2)$以下的修正.对于标量模式的引力摄动,我们找到了一个主变量,并研究了它的频谱,提供了我们的方案的有效性制度的分析。我们表明,不稳定性持续列入$R^2$ -校正,临界波长增加值的$α/r_+^2<<1$,提供了新的证据的现象已经观察到在其他方法。我们还构造了提升的黑弦,并计算了由于高曲率项对质量、动量和张力的修正。量纲耦合$α$的存在破坏了Smarr关系式的有效性,Smarr关系式是欧拉关系式的引力版本,它必须对每个均匀的热力学系统都成立。我们表明,这种身份可以恢复工作在一个扩展的热力学设置,包括高斯-邦纳耦合的变化。

英文摘要:

We consider a perturbative Gauss-Bonnet term supplementing the Einstein-Hilbert action, and evaluate its effect on the spectrum of the scalar mode that triggers the Gregory-Laflamme instability of black strings in five dimensional General Relativity. After studying some properties of the static black string, we provide the correction to the Lichnerowicz operator up to $\mathcal{O}(α^2)$. For the scalar mode of the gravitational perturbation, we find a master variable and study its spectrum, providing an analysis of the regime of validity of our scheme. We show that the instability persists under the inclusion of the $R^2$-correction, and that the critical wavelength increases with the value of $α/r_+^2<<1$, providing new evidence of the phenomenon which was already observed in other approaches. We also construct the boosted black strings and compute the correction to the mass, the momentum and the tension due to the higher curvature term. The presence of the dimensionful coupling $α$ spoils the validity of the Smarr relation, which is the gravitational version of the Euler relation which must hold for every homogeneous, thermodynamic system. We show that this identity can be restored by working in an extended thermodynamic setup that includes variations of the Gauss-Bonnet coupling.

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