arXiv 0910.44082009-10-22hep-thgr-qc

Schwarzschild黑洞的超对称推广

Towards a Supersymmetric Generalization of the Schwarzschild Black Hole

J. C. López-Domínguez, O. Obregón, S. Zacarías

备注：: 20 pages, REVTeX4, Accepted to be published in Physical Review D
发表信息：: Phys.Rev.D80:104020,2009
DOI：: 10.1103/PhysRevD.80.104020

摘要：

Kantowski-Sachs模型的Wheeler-DeWitt（WDW）方程也可以理解为Schwarzschild黑洞的WDW方程，因为这两个度量之间存在着众所周知的同构关系。WDW方程及其解与我们使用的坐标片是“不相容的”，只有通过施加坐标条件，我们才能区分宇宙模型和黑洞模型。此时，叶理参数$t$或$r$将出现在目标解中。在这项工作中，我们超对称化这个WDW方程获得额外的长期潜在的两个可能的迹象。然后应用WKB方法，得到两个经典方程。它表明，事件视界永远不能达到，因为非常接近它的额外项的潜力，为每一个方程，是更相关的一个对应于史瓦西。然后，我们可以研究渐近的情况下，其中的两个项之一的哈密顿主导的行为。其中一个对应于通常的史瓦西黑洞。我们将在这里研究另外两个渐近区域，它们提供了三个解。它们都在$r=0$中有一个奇点，并且根据积分常数$C$，它们也可以在$r=C^2$中存在奇点。这两种解都没有牛顿极限。我们研究的黑洞解在奇点$r=C^2$和最大半径$r_m$之间进行了分析。我们发现一个相关的质量，考虑到相关的宇宙学解决方案内$r=C^2$，和基于全息原理的熵可以分配给这个渐近解。

英文摘要：

The Wheeler-DeWitt (WDW) equation for the Kantowski-Sachs model can also be understood as the WDW-equation corresponding to the Schwarzschild black hole due to the well known diffeomorphism between these two metrics. The WDW-equation and its solutions are ``ignorant'' of the coordinate patch one is using, only by imposing coordinate conditions we can differentiate between cosmological and black hole models. At that point, the foliation parameter $t$ or $r$ will appear in the solution of interest. In this work we supersymmetrize this WDW-equation obtaining an extra term in the potential with two possible signs. The WKB method is then applied, given rise to two classical equations. It is shown that the event horizon can never be reached because, very near to it the extra term in the potential, for each one of the equations, is more relevant than the one that corresponds to Schwarzschild. One can then study the asymptotic cases in which one of the two terms in the Hamiltonian dominates the behavior. One of them corresponds to the usual Schwarzschild black hole. We will study here the other two asymptotic regions; they provide three solutions. All of them have a singularity in $r=0$ and depending on an integration constant $C$ they can also present a singularity in $r=C^2$. Neither of these solutions have a Newtonian limit. The black hole solution we study is analyzed between the singularity $r=C^2$ and a maximum radius $r_m$. We find an associated mass, considering the related cosmological solution inside $r=C^2$, and based on the holographic principle an entropy can be assigned to this asymptotic solution.

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