The Linear Stability of Reissner–Nordström Spacetime: The Full Subextremal Range $$|Q|,Communications in Mathematical Physics

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The Linear Stability of Reissner–Nordström Spacetime: The Full Subextremal Range $$|Q|
Communications in Mathematical Physics ( IF 2.2 ) Pub Date : 2020-11-03 , DOI: 10.1007/s00220-020-03893-z
Elena Giorgi

We prove the linear stability of subextremal Reissner-Nordstrom spacetimes as solutions to the Einstein-Maxwell equation. We make use of a novel representation of gauge-invariant quantities which satisfy a symmetric system of coupled wave equations. This system is composed of two of the three equations separately derived in previous works, where the estimates required arbitrary smallness of the charge. Here, the estimates are obtained by defining a combined energy-momentum tensor for the system in terms of the symmetric structure of the right hand sides of the equations. We obtain boundedness of the energy, Morawetz estimates and decay for the full subextremal range |Q|

中文翻译：

Reissner-Nordström 时空的线性稳定性：完整的次极值范围 $$|Q|

我们证明了作为爱因斯坦-麦克斯韦方程解的次极值 Reissner-Nordstrom 时空的线性稳定性。我们使用满足耦合波动方程对称系统的规范不变量的新表示。该系统由之前工作中分别推导出的三个方程中的两个组成，其中估计需要任意小的电荷。此处，通过根据方程右侧的对称结构定义系统的组合能量-动量张量来获得估计值。我们获得了能量的有界性、Morawetz 估计和整个次极值范围的衰减|Q|

更新日期：2020-11-03

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