The large D limit of General Relativity
The large D limit of General Relativity
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DOI：
10.1007/jhep06(2013)009
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发表时间：
2013-02
影响因子：
5.4
通讯作者：
R. Emparan;Ryo Suzuki;Kentaro Tanabe
中科院分区：
文献类型：
--
作者：
R. Emparan;Ryo Suzuki;Kentaro Tanabe
广义相对论在时空维度D的数量无限大的限制下进行了极大的简化：它简化为一种非相互作用粒子的理论，这些粒子的半径有限，但横截面却小得几乎消失，它们既不发射也不吸收任何有限频率的辐射。非平凡的黑洞动力学发生在长度尺度小于视界半径的1/D倍，频率大于视界半径的倒数的D倍。由于视界附近引力势的梯度很大，在大D处尺度的分离使得黑洞动力学理论有效。本文将这种有效的描述推广到1/D高阶，并解析地计算了标量吸收几率。我们解决了下一个到下一个到领先的顺序的黑膜不稳定性，非常准确的结果，提高了以前的近似与其他方法。这些例子表明，可以制定在任意数量的维度的问题可能是易于处理的分析形式，并非常有效地，所以，在大D扩展。
General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.