Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: an exact vacuum solution in five dimensions
Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: an exact vacuum solution in five dimensions
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DOI：
10.1088/0264-9381/26/6/065002
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发表时间：
2009-03-21
影响因子：
3.5
通讯作者：
Troncoso, Ricardo
中科院分区：
文献类型：
--
作者：
Anabalon, Andres;Deruelle, Nathalie;Troncoso, Ricardo
众所周知，Kerr-Schild度规使爱因斯坦张量线性化。我们将在这里看到，它们还简化了高斯-邦纳张量，当种子度量最大对称时，高斯-邦纳张量在任意克尔-希尔德函数f中仅是二次的。当种子度规是球坐标系中具有任意参数a和B的五维最大对称时空时，这个性质使我们能够给出它的迹的一个简单的解析表达式。当种子度规是平坦的并且扁率参数相等时，我们也以（相当）简单的形式写出完整的爱因斯坦-高斯-邦纳张量（带有宇宙学项），a = B。利用这些结果，我们给出了具有宇宙项和不等于B的Einstein-Gauss-Bonnet场方程的迹的紧致解。然后，我们检查是否这个解决方案的跟踪没有解决其余的场方程。我们发现，它不一般，除非高斯-邦纳耦合是这样的场方程有一个唯一的最大对称的解决方案。
As is well known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five-dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a = b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a not equal b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.