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arXiv 1504.07580gr-qc
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关于Dirichlet壁的引力稳定性

On the stability of gravity with Dirichlet walls

Tomas Andrade, William R. Kelly, Donald Marolf, Jorge E. Santos

摘要:

狄利克雷墙--在有限距离处的类时边界,在其上诱导度规是固定的--已经被用来模拟具有有限截止的AdS时空。在规范/引力对偶的背景下,这样的模型通常被描述为对偶于一些新的UV-cufoff版本的相应的CFT,保持局部洛伦兹不变性。我们研究了存在这样一个壁的线性引力,发现它与自旋为零和一的场的Dirichlet边界条件的类似情况有显著的不同。特别是,使用Kodama-Ishibashi形式主义,必须施加在标量扇区主场与谐波时间依赖的边界条件明确地取决于它们的频率。这一特征首先出现在自旋为2的情况下,似乎与运动方程的二阶性质有关。它引起了一些新的不稳定性,虽然全球和平面Anti-de Sitter保持(线性)稳定的存在下,大半径Dirichlet截止。不稳定性出现在球形狄利克雷壁的外侧,也出现在de Sitter空间中足够大的球形壁的内侧。我们分析了在闵可夫斯基空间、德西特空间和反德西特空间以及某些黑洞时空中的平壁和球壁的内部和外部,并发现了上述情况下的稳定性。特别是,我们发现没有线性不稳定性的存在下,平坦的墙壁。我们还发现了支持中性黑洞被狄利克雷壁排斥的猜想的证据。

英文摘要:

Dirichlet walls -- timelike boundaries at finite distance from the bulk on which the induced metric is held fixed -- have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often described as dual to some novel UV-cufoff version of a corresponding CFT that maintains local Lorentz invariance. We study linearized gravity in the presence of such a wall and find it to differ significantly from the seemingly-analogous case of Dirichlet boundary conditions for fields of spins zero and one. In particular, using the Kodama-Ishibashi formalism, the boundary condition that must be imposed on scalar-sector master field with harmonic time dependence depends explicitly on their frequency. That this feature first arises for spin-2 appears to be related to the second-order nature of the equations of motion. It gives rise to a number of novel instabilities, though both global and planar Anti-de Sitter remain (linearly) stable in the presence of large-radius Dirichlet cutoffs. The instabilities arise on the outside of spherical Dirichlet walls, and also inside sufficiently large such spherical walls in de Sitter space. We analyze both inside and outside of flat and spherical walls in Minkowski, de Sitter, and anti-de Sitter space, as well as in certain black hole spacetimes and find stability for cases not mentioned above. In particular, we find no linear instabilities in the presence of flat walls. We also find evidence supporting the conjecture that neutral black holes are repelled by Dirichlet walls.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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