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Accurate quasinormal modes of the five-dimensional Schwarzschild-Tangherlini black holes
Physical Review D ( IF 5 ) Pub Date : 2021-10-18 , DOI: 10.1103/physrevd.104.084066
Jerzy Matyjasek

The objective of this paper is to construct the accurate (say, to 11 decimal places) frequencies of the quasinormal modes of the five-dimensional Schwarzschild-Tangherlini black hole using three major techniques: the Hill determinant method, the continued fractions method, and the WKB-Padé method and to discuss the limitations of each. It is shown that for the massless scalar, gravitational tensor, gravitational vector, and electromagnetic vector perturbations considered in this paper, the Hill determinant method and the method of continued fractions (both with the convergence acceleration) always give identical results, whereas the WKB-Padé method gives the results that are amazingly accurate in most cases. Notable exception are the gravitational vector perturbations (j=2 and =2), for which the WKB-Padé approach apparently does not work. Here we have an interesting situation in which the WKB-based methods (WKB-Padé and WKB–Borel–Le Roy) give the complex frequency that differs from the result obtained within the framework of the continued fraction method and the Hill determinant method. For the fundamental mode, deviation of the real part of frequency from the exact value is 0.5% whereas the deviation of the imaginary part is 2.7%. For 3 the accuracy of the WKB results is similar again to the accuracy obtained for other perturbations. The case of the gravitational scalar perturbations is briefly discussed.

中文翻译:

五维 Schwarzschild-Tangherlini 黑洞的精确准正规模式

本文的目的是使用三种主要技术构建五维 Schwarzschild-Tangherlini 黑洞准正规模式的准确(比如小数点后 11 位)频率:希尔行列式方法、连分数方法和WKB-Padé 方法并讨论每种方法的局限性。结果表明,对于本文考虑的无质量标量、引力张量、引力矢量和电磁矢量扰动,Hill行列式方法和连分数方法(均具有收敛加速度)总是给出相同的结果,而WKB- Padé 方法在大多数情况下给出了惊人的准确结果。值得注意的例外是引力矢量扰动(j=2=2),WKB-Padé 方法显然不起作用。这里我们有一个有趣的情况,其中基于 WKB 的方法(WKB-Padé 和 WKB-Borel-Le Roy)给出的复频率与在连分数法和希尔行列式方法框架内获得的结果不同。对于基模,频率实部与精确值的偏差为 0.5%,而虚部的偏差为 2.7%。为了3WKB 结果的准确性再次与其他扰动获得的准确性相似。简要讨论了引力标量扰动的情况。
更新日期:2021-10-19
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