论文标题
Codazzi张量及其空间时间和棉花重力
Codazzi tensors and their space-times, and Cotton gravity
论文作者
论文摘要
我们研究某些Codazzi张量的几何特性是为了自身的缘故，以及它们出现在最近的棉花重力理论中。我们证明，当且仅当指标是广义的Stephani宇宙时，我们就证明了完美的流体张量是Codazzi。痕量状况将其限制为扭曲的时空，如Merton和Derdzinski所证明的那样。我们还为时空提供了必要和足够的条件，以托管当前流量的Codazzi张量。特别是，我们研究了包括Nariai和Bertotti-Robinson指标在内的静态和球体对称情况。后者是Yang纯空间时间的特殊情况，以及具有恒定曲率标量的空间平坦的FRW空间时间。我们将这些结果应用于原田最近的棉花重力。方程有选择的自由，可以选择一种codazzi张量，从而限制了该理论上演的时空。对物理学有意义的形式选择的张量意味着Ricci张量的形式，两者指定了能量弹药张量，这是所选度量标准的棉花重力的来源。例如，Stephani，Nariai和Bertotti-Robinson太空时期用物理明智的能量量张量解决棉花重力。最后，我们讨论了保姆太空时期的棉花重力。
We study the geometric properties of certain Codazzi tensors for their own sake, and for their appearance in the recent theory of Cotton gravity. We prove that a perfect-fluid tensor is Codazzi if and only if the metric is a generalized Stephani universe. A trace condition restricts it to a warped space-time, as proven by Merton and Derdzinski. We also give necessary and sufficient conditions for a space-time to host a current-flow Codazzi tensor. In particular, we study the static and spherically symmetric cases, which include the Nariai and Bertotti-Robinson metrics. The latter are a special case of Yang Pure space-times, together with spatially flat FRW space-times with constant curvature scalar. We apply these results to the recent Cotton gravity by Harada. The equations have the freedom of choosing a Codazzi tensor, that constrains the space-time where the theory is staged. The tensor, chosen in forms significative for physics, implies the form of the Ricci tensor, and the two specify the energy-momentum tensor, which is the source in Cotton gravity for the chosen metric. For example, the Stephani, Nariai and Bertotti-Robinson space-times solve Cotton gravity with physically sensible energy-momentum tensors. Finally, we discuss Cotton gravity in De Sitter space-times.
