A Dialogue of multipoles: Matched asymptotic expansion for caged black holes
A Dialogue of multipoles: Matched asymptotic expansion for caged black holes
复制标题
多极对话：笼中黑洞的匹配渐近膨胀
DOI：
10.1088/1126-6708/2004/06/053
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发表时间：
2004
影响因子：
5.4
通讯作者：
B. Kol
中科院分区：
文献类型：
--
作者：
Dan Gorbonos;B. Kol
到目前为止，还没有一个已知的解析解来解释在紧致维中的黑洞。我们发展了一个解析微扰理论，其中的小参数是黑洞的大小相对于紧凑的尺寸。我们建立了一个一般程序的任意阶的扰动系列的基础上的渐近匹配展开两个坐标补丁：近地平线区和渐近区。该过程是在每个区域中的普通扰动展开，其中另外一些边界数据来自另一个区域，因此该过程在区域之间交替。它可以被看作是一个多极的对话，其中黑洞改变它的形状（质量多极），以响应由其周期性的“镜子”所产生的场（多极），并反过来改变其字段等。我们提出了领先的全度规的修正，包括面积-温度关系的第一个修正，黑洞偏心率和“阿基米德效应”的领先项。下一个订单更正将出现在续集。在我们的方式独立地确定静态扰动的史瓦西黑洞在d维？5、方程组在哪里可以简化为“一个主方程”？一个简单的常微分方程解决方案是超几何函数，在某些情况下减少到多项式。
No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic ``mirrors'', and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the ``Archimedes effect''. The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d ? 5, where the system of equations can be reduced to ``a master equation'' ? a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.