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arXiv 0712.3308gr-qchep-th
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超对称孤立视界

Supersymmetric isolated horizons

Tomas Liko, Ivan Booth

备注：
26 pages, 1 figure; v2: typos corrected, topology arguments corrected, discussion of black rings and dipole charge added, references added, version to appear in Classical and Quantum Gravity
发表信息：
Class.Quant.Grav.25:105020,2008
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摘要：

在所有（奇）$D\geq5$维下，构造了Einstein-Maxwell-Chern-Simons理论中旋转弱孤立视界的协变相空间.特别是，我们表明，相应的相空间上的视界满足黑洞力学的第零和第一定律。我们证明了在四维（当去掉陈-西蒙斯项时）和五维中孤立视界上的Killing旋量的存在要求视界上的诱导（法向）联系必须为零，这反过来又意味着表面引力和旋转的一种形式为零。这意味着视界角动量的引力分量为零，而电磁分量（归因于体辐射场）不受约束。由此可见，孤立视界只有当它是极值的且不旋转时才是超对称的。这些视界的一个显著性质是，Killing旋量只需要存在于视界本身。它不一定存在于地平线之外。此外，我们发现，当视界的表面引力为零时的极限提供了一个拓扑约束。具体地说，当主能量条件满足且宇宙学常数$Λ$为零或正值时，视界横截面的标量曲率的积分必须为正，特别是排除了超对称孤立视界的环面拓扑（除非$Λ<0$）当且仅当应力-能量张量$T_{ab}$的形式是，对于任何两个零矢量$\ell$和$n$，$T_{ab}\ell^{a}n^{b}=0$具有在视界上的归一化$\ell_{a}n^{a}=-1$。

英文摘要：

We construct a covariant phase space for rotating weakly isolated horizons in Einstein-Maxwell-Chern-Simons theory in all (odd) $D\geq5$ dimensions. In particular, we show that horizons on the corresponding phase space satisfy the zeroth and first laws of black-hole mechanics. We show that the existence of a Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons term is dropped) and in five dimensions requires that the induced (normal) connection on the horizon has to vanish, and this in turn implies that the surface gravity and rotation one-form are zero. This means that the gravitational component of the horizon angular momentum is zero, while the electromagnetic component (which is attributed to the bulk radiation field) is unconstrained. It follows that an isolated horizon is supersymmetric only if it is extremal and nonrotating. A remarkable property of these horizons is that the Killing spinor only has to exist on the horizon itself. It does not have to exist off the horizon. In addition, we find that the limit when the surface gravity of the horizon goes to zero provides a topological constraint. Specifically, the integral of the scalar curvature of the cross sections of the horizon has to be positive when the dominant energy condition is satisfied and the cosmological constant $Λ$ is zero or positive, and in particular rules out the torus topology for supersymmetric isolated horizons (unless $Λ<0$) if and only if the stress-energy tensor $T_{ab}$ is of the form such that $T_{ab}\ell^{a}n^{b}=0$ for any two null vectors $\ell$ and $n$ with normalization $\ell_{a}n^{a}=-1$ on the horizon.

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