The Massive Wave Equation in Asymptotically AdS Spacetimes
The Massive Wave Equation in Asymptotically AdS Spacetimes
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DOI：
10.1007/s00220-013-1720-3
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发表时间：
2012-02
影响因子：
2.4
通讯作者：
C. Warnick
中科院分区：
文献类型：
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作者：
C. Warnick
我们考虑渐进 AdS 空间上的大规模波动方程。我们表明，类时 $${\fancyscript{F}}$$ 的行为类似于有限类时边界，在该边界上，可以对一系列（负）质量参数（包括共形耦合情况）施加狄利克雷、诺伊曼或罗宾条件的等效条件。我们证明了在 H1 规律性水平上相关初始边值问题的适定性。我们还证明可以获得更高的正则性，以及 $${\fancyscript{F}}$$ 附近场的渐近展开。这些证明依赖于能量方法，该方法是针对 Breitenlohner 和 Freedman 引入的修改能量而定制的。我们不假设时空是静止的，也不假设波动方程是分离的。
We consider the massive wave equation on asymptotically AdS spaces. We show that the timelike $${\fancyscript{F}}$$ behaves like a finite timelike boundary, on which one may impose the equivalent of Dirichlet, Neumann or Robin conditions for a range of (negative) mass parameter which includes the conformally coupled case. We demonstrate well posedness for the associated initial-boundary value problems at theH1level of regularity. We also prove that higher regularity may be obtained, together with an asymptotic expansion for the field near $${\fancyscript{F}}$$. The proofs rely on energy methods, tailored to the modified energy introduced by Breitenlohner and Freedman. We do not assume the spacetime is stationary, nor that the wave equation separates.