Cotton张量、黑洞熵和等变Pontryagin形式的守恒流
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
摘要：
三维流形M的度量空间中的Chern-Simons拉格朗日密度在M上的同态作用下不是不变的。然而，它的欧拉-拉格朗日算子可以与Cotton张量等同，这是不变的。由于拉格朗日量不是不变的，因此不能应用Noether定理来获得守恒流。我们表明，它是可能的，以获得一个等变的守恒电流的棉花张量通过使用第一等变庞特里亚金形式的束的度量。最后我们定义了一个哈密顿流，它给出了陈-西蒙斯项对黑洞熵、能量和角动量的贡献。
英文摘要：
The Chern-Simons lagrangian density in the space of metrics of a 3-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the lagrangian is not invariant, Noether Theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.
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