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arXiv 1408.0875hep-thgr-qc
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黑洞的Geroch群描述

Geroch Group Description of Black Holes

Bidisha Chakrabarty, Amitabh Virmani

摘要:

一方面,Geroch群允许我们将时空无关矩阵与引力组态联系起来,这些组态实际上只依赖于两个坐标。这类黑洞包括静止的轴对称四维和五维黑洞。另一方面,最近发展的逆散射方法允许一个因式分解这些矩阵明确地构建相应的时空配置。在这项工作中,我们证明了建设以及因式分解的Geroch群矩阵的广泛的一类黑洞的例子。特别地,我们得到了五维Myers-Perry和Kaluza-Klein黑洞的Geroch群SL(3,R)矩阵和四维Kerr-Newman黑洞的Geroch群SU(2,1)矩阵.我们还提出了一定的非平凡的Geroch群矩阵和这些黑洞的电荷矩阵之间的关系。

英文摘要:

On one hand the Geroch group allows one to associate spacetime independent matrices with gravitational configurations that effectively only depend on two coordinates. This class includes stationary axisymmetric four- and five-dimensional black holes. On the other hand, a recently developed inverse scattering method allows one to factorize these matrices to explicitly construct the corresponding spacetime configurations. In this work we demonstrate the construction as well as the factorization of Geroch group matrices for a wide class of black hole examples. In particular, we obtain the Geroch group SL(3,R) matrices for the five-dimensional Myers-Perry and Kaluza-Klein black holes and the Geroch group SU(2,1) matrix for the four-dimensional Kerr-Newman black hole. We also present certain non-trivial relations between the Geroch group matrices and charge matrices for these black holes.

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