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arXiv 1007.3209hep-thmath-phmath.MPnlin.SI
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超引力中的黑洞与可积性

Black holes in supergravity and integrability

W. Chemissany, P. Fré, J. Rosseel, A. S. Sorin, M. Trigiante, T. Van Riet

摘要:

无质量超引力理论中的静止黑洞是由目标空间上的测地线曲线描述的,该测地线曲线是经过时间降维后得到的。当目标空间是一个对称陪集空间时,我们利用群论结构,通过明确构造对合中正确数量的Hamilton算子,证明了二阶测地线方程在Liouville意义下是可积的.这意味着可以应用Hamilton-Jacobi形式,证明了所有这样的黑洞解,包括非极值解,都具有(假)超势的描述。此外,我们改进了现有的积分方法的建设的Lax积分算法,集成的二阶方程在一个步骤,而不是通常的两个步骤的过程。我们用一个具体的例子来说明这项技术。

英文摘要:

Stationary black holes of massless supergravity theories are described by certain geodesic curves on the target space that is obtained after dimensional reduction over time. When the target space is a symmetric coset space we make use of the group-theoretical structure to prove that the second order geodesic equations are integrable in the sense of Liouville, by explicitly constructing the correct amount of Hamiltonians in involution. This implies that the Hamilton-Jacobi formalism can be applied, which proves that all such black hole solutions, including non-extremal solutions, possess a description in terms of a (fake) superpotential. Furthermore, we improve the existing integration method by the construction of a Lax integration algorithm that integrates the second order equations in one step instead of the usual two step procedure. We illustrate this technology with a specific example.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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