The Vainshtein mechanism in the decoupling limit of massive gravity
The Vainshtein mechanism in the decoupling limit of massive gravity
复制标题
大重力解耦极限中的 Vainshtein 机制
DOI：
10.1088/1126-6708/2009/05/098
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发表时间：
2009
影响因子：
5.4
通讯作者：
R. Ziour
中科院分区：
文献类型：
--
作者：
E. Babichev;C. Deffayet;R. Ziour
我们研究了非线性质量引力的静态球对称解。我们首先确定，在一个适合于研究这些解的分析中，在Goldstone图像描述中使用的解耦极限（DL）的模拟。我们证明了DL中遗留的方程组具有正则解，其特征是广义相对论（GR）解的类vainshtein恢复。因此，在积分完整的非线性方程组时发现的奇点并不存在于DL中，尽管这些奇点通常被认为是由于在这个极限中也看到的负能量模式。此外，我们还证明了Vainshtein在小半径处推测的标度只是无限族非奇异解中的一种极限情况，每个非奇异解在Vainshtein半径以下都表现出GR解的Vainshtein恢复，而在小距离处则表现出不同的公共标度。这种新的缩放被证明与DL中遗留的非线性的零模式相关联。我们还表明，在深度学习中，即使在原始Vainshtein机制不起作用的情况下，这种缩放也允许恢复GR解。我们的结果表明，要么DL忽略了非线性质量引力的一些重要特征，要么完全非线性理论解的一些重要特征被忽略了。它们也可能为DGP模型和相关建议带来有趣的结果。
We investigate static spherically symmetric solutions of nonlinear massive gravities. We first identify, in an ansatz appropriate to the study of those solutions, the analog of the decoupling limit (DL) that has been used in the Goldstone picture description. We show that the system of equations left over in the DL has regular solutions featuring a Vainshtein-like recovery of solutions of General Relativity (GR). Hence, the singularities found to arise integrating the full nonlinear system of equations are not present in the DL, despite the fact those singularities are usually thought to be due to a negative energy mode also seen in this limit. Moreover, we show that the scaling conjectured by Vainshtein at small radius is only a limiting case in an infinite family of non singular solutions each showing a Vainshtein recovery of GR solutions below the Vainshtein radius but a different common scaling at small distances. This new scaling is shown to be associated with a zero mode of the nonlinearities left over in the DL. We also show that, in the DL, this scaling allows for a recovery of GR solutions even for potentials where the original Vainshtein mechanism is not working. Our results imply either that the DL misses some important features of nonlinear massive gravities or that important features of the solutions of the full nonlinear theory have been overlooked. They could also have interesting outcomes for the DGP model and related proposals.