arXiv 0905.39382009-05hep-th

D=4静态黑洞的一阶描述和Hamilton-Jacobi方程

First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation

L. Andrianopoli, R. D'Auria, E. Orazi, M. Trigiante

备注：: A clarifying discussion on the existence of the prepotential and a comment on multiple attractors are added; typos corrected, references added
发表信息：: Nucl.Phys.B833:1-16,2010
DOI：: 10.1016/j.nuclphysb.2010.02.020

摘要：

本文讨论了Hamilton-Jacobi方法在四维球对称静态黑洞一阶描述中的应用。特别是，我们表明，前势流的特点与汉密尔顿主函数相关联的一维有效拉格朗日相一致。这意味着预势总是可以定义的，至少在局部的径向变量和模空间，无论是在极值和非极值的情况下，并允许我们得出结论，它是对偶不变的。在此框架下，我们给出了“Weinhold度量”的一般定义，并由此给出了多个吸引子存在的必要条件。Hamilton-Jacobi形式既可以应用于电磁势已被积分的受限相空间，也可以应用于使用所谓的三维欧几里德方法将电磁势对偶化为标量场的情况。我们给出了一些应用的形式主义的例子，无论是对BPS和非BPS的黑洞。

英文摘要：

In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides with the Hamilton principal function associated with the one-dimensional effective Lagrangian. This implies that the prepotential can always be defined, at least locally in the radial variable and in the moduli space, both in the extremal and non-extremal case and allows us to conclude that it is duality invariant. We also give, in this framework, a general definition of the ``Weinhold metric'' in terms of which a necessary condition for the existence of multiple attractors is given. The Hamilton-Jacobi formalism can be applied both to the restricted phase space where the electromagnetic potentials have been integrated out as well as in the case where the electromagnetic potentials are dualized to scalar fields using the so-called three-dimensional Euclidean approach. We give some examples of application of the formalism, both for the BPS and the non-BPS black holes.

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