Kerr 黑洞中的準正則模
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2008
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Abstract
我們利用Teukolsky's radial方程式的解，在複數平面沿著兩條同屬於相同同倫類的路徑做解析連續，其波函數的monodromy必須是相同的，藉此得到Kerr黑洞中的準正則模，而且我們的結果和利用WKB方法所得到的是一致的。我們更進一步討論藉著展開零階的波方程，去計算4維Kerr黑洞準正則模漸進行為的系統性方法。
We analytically derive quasi-normal frequencies for Kerr black hole by analytically continuing the relevant solution of Teukolsky's radial equation to the complex plane, matching the monodromy of the wave function along two different contours in the same homotopy class. Our results are in agreement with the results from WKB. We also discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of four-dimensional Kerr black hole by expanding around the zeroth-order approximation to the wave equation.
We analytically derive quasi-normal frequencies for Kerr black hole by analytically continuing the relevant solution of Teukolsky's radial equation to the complex plane, matching the monodromy of the wave function along two different contours in the same homotopy class. Our results are in agreement with the results from WKB. We also discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of four-dimensional Kerr black hole by expanding around the zeroth-order approximation to the wave equation.
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黑洞, 準正則模, 一階修正, 量子重力, Black Holes, Quasi-normal Modes, First-order Corrections, Quantum Gravity