Quasinormal modes of black holes were previously calculated in a non-linear electrodynamics and in the Gauss-Bonnet gravity theory. Here we take into consideration both of the above factors and find quasinormal modes of a (massive) scalar field in the background of a black hole in the five-dimensional Einstein-Gauss-Bonnet gravity coupled to a non-linear electrodynamics having Maxwellian weak-field limit. For the non-linear electrodynamics we considered the high frequency (eikonal) regime of oscillations analytically, while for the lower multipoles the higher order WKB analysis with the help of Pad\'{e} approximants and the time domain integration were used. We found that perturbations of a test scalar field violate the inequality between the damping rate of the least damped mode and the Hawking temperature, known as the Hod's proposal. This does not exclude the situation in which gravitational spectrum may restore the Hod's inequality, so that only the analysis of the full spectrum, including gravitational perturbations, will show if the quasinormal modes we found here for the scalar field can be a counterexample to the Hod's conjecture or not. We also revealed that in such a system, which includes the higher curvature corrections and non-linear electrodynamics, for perturbations of a massive scalar field there exists the phenomenon of the arbitrary long lived quasinormal modes - quasiresonances.

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结合非线性电动力学的 5D Gauss-Bonnet 引力中黑洞的准正规模式

黑洞的准正态模式以前是在非线性电动力学和高斯-博内引力理论中计算出来的。在这里，我们考虑上述两个因素，并在与具有麦克斯韦弱的非线性电动力学耦合的五维爱因斯坦-高斯-博内引力中的黑洞背景中找到（大质量）标量场的准正规模式。场限制。对于非线性电动力学，我们分析地考虑了振荡的高频（本征）状态，而对于较低的多极子，则使用了借助 Pad\'{e} 近似值和时域积分的高阶 WKB 分析。我们发现测试标量场的扰动违反了最小阻尼模式的阻尼率与霍金温度之间的不等式，称为霍德建议。这并不排除引力谱可以恢复 Hod 不等式的情况，因此只有对包括引力扰动在内的全谱的分析才能表明我们在这里找到的标量场的准正规模式是否可以作为 Hod 不等式的反例猜想与否。我们还揭示了在这样一个系统中，包括更高的曲率校正和非线性电动力学，对于大量标量场的扰动，存在任意长寿命准正规模式 - 准谐振的现象。将显示我们在此处为标量场找到的准正规模式是否可以作为 Hod 猜想的反例。我们还揭示了在这样一个系统中，包括更高的曲率校正和非线性电动力学，对于大量标量场的扰动，存在任意长寿命准正规模式 - 准谐振的现象。将显示我们在此处为标量场找到的准正规模式是否可以作为 Hod 猜想的反例。我们还揭示了在这样一个系统中，包括更高的曲率校正和非线性电动力学，对于大量标量场的扰动，存在任意长寿命准正规模式 - 准谐振的现象。