论文标题
在服用$ d \至4 $的高斯 - 骨网限制时：理论与解决方案
On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
论文作者
论文摘要
我们在四个维度上评论了最近引入的高斯河网重力。我们认为，考虑该理论是由一组$ d \至4 $的较高维高斯重力解决方案来定义的，这是没有意义的。我们表明，明确定义的$ d \至4 $高斯重力的极限是获得了曼恩和罗斯采用的一种方法，以在$ d = 2 $尺寸中获得爱因斯坦重力的极限。这是通过尺寸还原方法获得的Horndeski类型的标量调整理论。通过考虑除球形对称性（taub-nut空间）以外的简单空间，我们表明，高维理论对四个维度的天真限制并不是很好地定义，并将结果指标与新理论的实际解决方案进行了对比。
We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of $D\to 4$ solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined $D\to 4$ limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in $D=2$ dimensions. This is a scalar-tensor theory of the Horndeski type obtained by a dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to four dimensions is not well defined and contrast the resultant metrics with the actual solutions of the new theory.
