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arXiv 2106.01412gr-qc
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一般非线性电动力学中带电黑洞的引力辐射和电磁辐射

Gravitational and electromagnetic radiation from an electrically charged black hole in general nonlinear electrodynamics

Ramin G. Daghigh, Michael D. Green

摘要:

在一般非线性电动力学的框架下,导出了带电荷的黑洞的电磁场和引力场耦合的奇、偶宇称扰动方程。拉格朗日密度是电磁场的洛伦兹不变标量的通用函数。我们在计算中加入了电磁场张量的Hodge对偶和宇宙学常数。对于每种类型的宇称,我们减少了系统的爱因斯坦场方程耦合到非线性电动力学的两个耦合薛定谔型波动方程,一个引力场和电磁场之一。导出了电磁场的Hodge对偶存在时的稳定性条件。

英文摘要:

We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equations, one for the gravitational field and one for the electromagnetic field. The stability conditions in the presence of the Hodge dual of the electromagnetic field are derived.

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