在高維克爾黑洞時空下的測地線

Geodesic in Higher Dimensional Spacetime of Kerr Black Holes

任國綸(Kuo-Lun Jen)

指導教授 ： 曹慶堂

淡江大學/理學院/物理學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00465

摘要

我們主要的工作是討論在高維Kerr時空下的穩定圓軌道存在性
問題。但由於高維Kerr時空的測地線方程複雜難解，也因為在高於
六維以上的Kerr黑洞具有“黑洞角動量無上限”的特性，因此我們
在本篇論文中會以六維一旋轉方向的Kerr黑洞時空為背景，來簡化
測地線方程的複雜度，進而討論在此時空下赤道面上的穩定圓軌道
存在性問題。此外，我們還會對測地線方程做黑洞角動量很大的極
限處理並討論在一般情形下的穩定圓軌道存在性問題以及測地線方
程的變化行為。最後，我們繪出依各運動常數變化的effective potential 圖形，來考量在一般情形下，穩定圓軌道的存在性問題。

關鍵字

測地線 ； 高維 ； 克爾黑洞

並列摘要

Our main work is to discuss the existence problem of stability circular orbit in higher dimensional Kerr spacetimes. The corresponding geodesics are complicated and difficult to solve. On the other hand, there is no upper limit on the angular momenta of Kerr black holes in dimensions higher than six. Thus, we simplify the geodesic by choosing to work with six dimensional Kerr black holes with one rotation direction in this thesis. We first discuss the existence problem of stability circular orbit in equatorial plane. Furthermore, we deal with the geodesic using a perturbative expansion when the angular momentum of the Kerr black hole is large in order to discuss the existence problem of stability circular orbit in general(not in equatorial plane) and the behavior of the geodesic. Finally, we plot the effective potentials for various of the constants of motion to consider the existence problem of stable circular orbit in general case.

並列關鍵字

Geodesic ； Higher dimension ； Kerr black holes

參考文獻

in a space-time of five-dimensional rotating black

hole,”Phys Rev.D 68 064011

black-hole spacetimes in all dimensions,”

[3] R. C. Myers and M. J. Perry,“Black Holes in Higher

Dimensional Space-Time,”Annals of Phys