arXiv 1003.60172010-03hep-thastro-ph.HEgr-qc

Chern-Simons修正引力的黑弦和Gödel型解

Black String and Gödel type Solutions of Chern-Simons Modified Gravity

Haji Ahmedov, Alikram N. Aliev

备注：: 18 pages, REVTeX; Some clarifications made, new references added
发表信息：: Phys.Rev.D82:024043,2010
DOI：: 10.1103/PhysRevD.82.024043

摘要：

在Chern-Simons（CS）修正引力理论中，给定CS标量场，不允许视界具有球拓扑的旋转黑洞解.在本文中，我们表明，它确实承认旋转{ \it黑洞/弦}的解决方案与圆柱拓扑的视界，并提出了两个有趣的物理例子，这样的配置。首先，我们证明了在三维引力的Banados-Teitelboim-Zanelli（BTZ）黑洞度规上增加一个类空平坦维所得到的BTZ定常黑弦，无论CS标量场的选择如何，它都能求解具有特定源项和{ \it}的CS修正引力场方程.其次，我们考虑了广义相对论中旋转直黑弦的Lemos解，并证明了当CS标量场仅为径向坐标的函数时，该解在CS修正引力下仍然存在。我们还讨论了CS修正引力中哥德尔型度规的两个例子，将三维引力的一个一般的单参数哥德尔型解族提升到四维。第一个例子是通常的广义相对论的哥德尔解，它也存在于CS修正引力中，CS标量场取决于两个变量，径向和方位角坐标。第二个例子给出了CS修正引力真空场方程的一个新的非平凡（非广义相对论）Gödel型解。这个解起源于拓扑大质量引力的相应真空解，当通过添加额外的空间坐标并选择CS标量场作为该坐标的线性函数将其扩展到四维时。

英文摘要：

Chern-Simons (CS) modified gravity with a prescribed CS scalar field does not admit rotating black hole solutions with spherical topology of the horizon. In this paper, we show that it does admit rotating {\it black hole/string} solutions with cylindrical topology of the horizon and present two intriguing physical examples of such configurations. First, we show that the Banados-Teitelboim-Zanelli (BTZ) stationary black string, that is obtained by adding on a spacelike flat dimension to the BTZ black hole metric of three-dimensional gravity, solves the field equations of CS modified gravity with a specific source term and {\it irrespective of the choice of CS scalar field}. Next, we consider the Lemos solution for a rotating straight black string in general relativity and show that for the CS scalar field being a function of the radial coordinate alone, this solution persists in CS modified gravity. We also discuss two examples of Gödel type metrics in CS modified gravity by uplifting to four dimensions a general one-parameter family of Gödel type solutions of three-dimensional gravity. The first example is the usual Gödel solution of general relativity which also survives in CS modified gravity with the CS scalar field depending on two variables, the radial and the azimuthal coordinates. The second example represents a new nontrivial (non general relativity) Gödel type solution to the vacuum field equations of CS modified gravity. This solution originates from the respective vacuum solution of topologically massive gravity when extending it to four dimensions by adding on an extra spatial coordinate and choosing the CS scalar field as a linear function of this coordinate.

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