It is well known that the theory of Cotton gravity proposed by Harada is trivially solved by all isotropic and homogeneous cosmologies. We show that this under-determination is more general. More precisely, the degree of arbitrariness in the solutions increases with the degree of symmetry. The inverse problem of finding the matter source generating a given spacetime geometry is similarly indeterminate in the case of highly symmetric configurations. We give two simple examples. The first is that of static spherically symmetric solutions, which depend on an arbitrary function of the radial coordinate. The second is that of anisotropic cosmologies, which depend on an arbitrary function of time.

中文翻译：

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棉花比重不能预测


众所周知，原田提出的棉花引力理论被所有各向同性和均匀宇宙学轻松解决。我们表明，这种不确定更为普遍。更准确地说，解的任意性程度随着对称度的增加而增加。在高度对称配置的情况下，找到生成给定时空几何的物质源的逆问题同样是不确定的。我们举两个简单的例子。第一种是静态球对称解，它依赖于径向坐标的任意函数。第二种是各向异性宇宙学，它依赖于时间的任意函数。