Black holes in supergravity and integrability
Black holes in supergravity and integrability
复制标题
超引力和可积性中的黑洞
DOI：
10.1007/jhep09(2010)080
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发表时间：
2010
影响因子：
5.4
通讯作者：
T. Riet
中科院分区：
文献类型：
--
作者：
W. Chemissany;P. Fré;J. Rosseel;A. Sorin;M. Trigiante;T. Riet
无质量超引力理论中的静止黑洞是由目标空间上经过时间降维后的特定测地线曲线来描述的。当目标空间是对称的协集空间时，我们利用群论结构，通过显式地构造对合中的哈密顿量，证明了二阶测地方程在Liouville意义上是可积的。这意味着可以应用Hamilton-Jacobi形式，证明所有此类黑洞解，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，构造了一种二阶方程的Lax积分算法，该算法将二阶方程的两步积分过程改为一步积分。我们用一个具体的例子来说明这种技术
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