Asymptotically anti-de Sitter spacetimes and conserved quantities in higher curvature gravitational theories
Asymptotically anti-de Sitter spacetimes and conserved quantities in higher curvature gravitational theories
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DOI：
10.1103/physrevd.71.084009
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发表时间：
2005-01
影响因子：
5
通讯作者：
N. Okuyama;J. Koga
中科院分区：
文献类型：
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作者：
N. Okuyama;J. Koga
在高曲率引力理论中，利用保角补全技术，考虑了n维渐近反de Sitter时空。我们首先论证了在高曲率引力理论中，应该补充一个关于Ricci张量的条件来定义渐近反de Sitter时空，并提出了渐近反de Sitter时空的另一种定义。基于这一定义，我们导出了引力场的守恒定律，并构造了两类高曲率引力理论中的守恒量。我们还证明了这些守恒量在与爱因斯坦引力相同的意义上满足平衡方程，并且它们复制了在其他地方得到的结果。这些守恒量被单独表示为Weyl张量的电子部分的积分，因此它们在纯粹的反de Sitter时空中同样消失，就像在爱因斯坦引力的情况下一样。
We consider $n$-dimensional asymptotically anti-de Sitter spacetimes in higher curvature gravitational theories with $n \geq 4$, by employing the conformal completion technique. We first argue that a condition on the Ricci tensor should be supplemented to define an asymptotically anti-de Sitter spacetime in higher curvature gravitational theories and propose an alternative definition of an asymptotically anti-de Sitter spacetime. Based on that definition, we then derive a conservation law of the gravitational field and construct conserved quantities in two classes of higher curvature gravitational theories. We also show that these conserved quantities satisfy a balance equation in the same sense as in Einstein gravity and that they reproduce the results derived elsewhere. These conserved quantities are shown to be expressed as an integral of the electric part of the Weyl tensor alone and hence they vanish identically in the pure anti-de Sitter spacetime as in the case of Einstein gravity.