Decay of weakly charged solutions for the spherically symmetric Maxwell-Charged-Scalar-Field equations on a Reissner-Nordström exterior space-time
Decay of weakly charged solutions for the spherically symmetric Maxwell-Charged-Scalar-Field equations on a Reissner-Nordström exterior space-time
复制标题
Reissner-Nordström 外部时空球对称麦克斯韦带电标量场方程弱带电解的衰变
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Moortel
中科院分区：
文献类型：
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作者：
M. Moortel
本文研究了具有球对称初值的（非线性）Maxwell荷电标量场方程在固定次极值Reissner-Nordstr”o m外时空上的Cauchy问题.证明了当麦克斯韦方程的电荷足够小时，该解是有界的，并以逆多项式速率衰减到类时无穷大和沿着黑洞视界.这个条件是特别满足的能量空间中的小数据，享受一个足够的衰减到渐近平坦的结束。
我们证明的一些衰减估计任意地接近于在电荷趋向于0 $的极限中的约束最优速率，遵循Hod和皮兰，arXiv：gr-qc/9712041的方法。
我们的结果也可以被解释为一个步骤的稳定性Reissner-Nordstr”{o}m黑洞的引力耦合Einstein-Maxwell-Charged-Scalar-Field模型。这个问题与对强宇宙审查的理解和在这种背景下的带电引力坍缩密切相关。
We consider the Cauchy problem for the (non-linear) Maxwell-Charged-Scalar-Field equations with spherically symmetric initial data, on a fixed sub-extremal Reissner-Nordstr"{o}m exterior space-time. We prove that the solutions are bounded and decay at an inverse polynomial rate towards time-like infinity and along the black hole event horizon, provided the charge of the Maxwell equation is sufficiently small. This condition is in particular satisfied for small data in energy space that enjoy a sufficient decay towards the asymptotically flat end.
Some of the decay estimates we prove are arbitrarily close to the conjectured optimal rate in the limit where the charge tends to $0$, following the heuristics of Hod and Piran, arXiv:gr-qc/9712041.
Our result can also be interpreted as a step towards the stability of Reissner-Nordstr"{o}m black holes for the gravity coupled Einstein-Maxwell-Charged-Scalar-Field model. This problem is closely connected to the understanding of strong cosmic censorship and charged gravitational collapse in this setting.
DOI：
10.2140/paa.2019.1.263
发表时间：
2019
期刊：
Pure and Applied Analysis
影响因子：
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作者：
Gajic, Dejan;Luk, Jonathan
通讯作者：
Luk, Jonathan
影响因子：
3.7
作者：
Dafermos, Mihalis;Holzegel, Gustav;Rodnianski, Igor
通讯作者：
Rodnianski, Igor