Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
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DOI：
10.1103/physrevd.82.124030
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发表时间：
2010-04
影响因子：
5
通讯作者：
J. Oliva;Sourya Ray
中科院分区：
文献类型：
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作者：
J. Oliva;Sourya Ray
本文对任意维的引力六阶导数拉氏量进行了分类，其追踪场方程是二阶或三阶的。在前一种情况下，大于6维的拉格朗日量简化为6维欧拉密度和两个线性独立的三次外尔不变量的任意线性组合。在五维空间中，除了独立的三次Weyl不变量外，我们还得到了一个有趣的三次组合，其静态球对称时空的场方程是二阶的。在后一种情况下，在任意维中，我们得到两个组合，在三维中，相当于两个科顿张量的完全收缩。此外，我们还恢复了所有的共形异常在六个维度。最后，我们给出了其中一些拉格朗日函数的一般静态球对称解。
We classify all the six-derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six reduces to an arbitrary linear combination of the six-dimensional Euler density and the two linearly independent cubic Weyl invariants. In five dimensions, besides the independent cubic Weyl invariant, we obtain an interesting cubic combination, whose field equations for static spherically symmetric spacetimes are of second order. In the latter case, in arbitrary dimensions we obtain two combinations, which in dimension three, are equivalent to the complete contraction of two Cotton tensors. Moreover, we also recover all the conformal anomalies in six dimensions. Finally, we present the general static, spherically symmetric solution for some of these Lagrangians.