四維黑洞的全息描述

Holographic Descriptions of Four-dimensional Black Holes

鄒守峻(Shou-Jyun Zou)

指導教授 ： 陳江梅

國立中央大學/理學院/物理學系/博士(2012年)

摘要

在這篇論文中，我們討論黑洞和共形場(CFT)之間的對應關係。根據全息原理，對應的 CFT 至少比黑洞少一個維度，就如同 AdS_D/CFT_{D-1} 的對應關係。我們分析帶電黑洞，Reissner-Nordstrom（RN）和 Kerr-Newman（KN）的情形。我們知道近視界極端 Kerr 黑洞會有（warped）AdS_3幾何結構，類似的結構也出現在當 RN 黑洞放到 5 維空間的近視界極端情形。對於 RN 黑洞的例子，CFT_2的對應描述預計也有電荷參數。我們詳細探討這類形的對應。此外，我們的研究結果還表明，有兩個自然的對應描述 KN 黑洞各自對應旋轉和電荷參數。為確認這個現象，我們討論非極端 KN 黑洞的隱性二維共形對稱性。

關鍵字

黑洞 ； 全息原理 ； 共形場論

並列摘要

In this thesis, we discuss the correspondence between black holes and conformal field theory. According to the holographic principle, the associated dual CFT should be one-dimension less than the spacetime of black hole, as the usual AdS$_D$/CFT$_{D-1}$ correspondence. We generalize the analysis for the Kerr to the charged black holes, in particular Reissner-Nordstr"{o}m (RN) and Kerr-Newman (KN). Like a (warped) AdS$_3$ geometry appearing in the near horizon of extremal Kerr, the similar structure also shows up in the RN black hole when it is uplifted into 5D. Thus a CFT$_2$ description is expected also for the charge parameter. We explore this sector of the duality in details. Moreover, our results also suggest that there are two natural dual descriptions for the KN black holes corresponding the the associated rotating and charge parameters. To confirm this prospect, we have explored the hidden 2D conformal symmetries in the generic non-extremal KN black hole.

並列關鍵字

black hole ； conformal field theory ； holographic principle

參考文獻

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