引力理论中的线性模和黑洞性质的研究
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摘要
在本论文中,我们通过李代数的方法,构造了任意维度的AdS时空背景下的有质量和无质量的标量模,矢量模以及自旋为2的模的解。这些解会出现在一些一般维度的包含高阶曲率项的引力和超引力模型中。临界引力理论中包含的Log模解也可以求得。进一步的,我们通过一个递推关系可以得到任意整数自旋的AdS背景下的线性模解。经过验证,这些任意维度和自旋的解的表达式至少在11维都是正确的。通过对这些解进行分析研究,我们可以得到了其质量需要满足的无快子条件。这是一个一般的Breitenlohner-Freedman界。这些解的具体表达式对于相应的临界引力及其扩展的研究也会发挥重要的作用。另外,本论文中还研究了一些黑洞性质方面的问题。我们研究了带有4个荷的旋转黑洞(Cvetic-Youm解)中隐藏的共形对称性。通过找出SL(2,R)L×SL(2,R)的共形对称性,我们利用Cardy公式得到的熵与Bekenstein-Hawking熵相等,并指出标量粒子的散射截面与共形场论中的结果相同。这些观点有力的支持了Kerr/CFT的论断。我们还利用黑洞辐射的遂穿机制研究了信息丢失佯谬。我们得到了在考虑量子效应的情况下,黑洞辐射中不会发生信息丢失问题,整个黑洞的蒸发过程是熵守恒的。其中一个有趣的结论是考虑量子效应以后,黑洞并不能完全蒸发,结果必须保留一个残余物。
In this thesis, we construct the explicit solutions for the linearized massive and massless spin-2, vector and scalar modes around the AdS spacetimes in diverse dimen-sions. These modes may arise in extended gravities and super gravities with higher order curvature terms in general dimensions. Log modes in critical gravities can also be straightforwardly deduced. We analyze the properties of these modes and obain the tachyon-free condition, which is a generalization of the Breitenlohner-Freedman bound. These modes should be served as useful tools to study various properties of the gravity theories. On the other hand, we study some properties of black holes. We find the hidden conformal symmetry in a rotating black hole with 4 charges (Cvetic-Youm solution). After reveiving the SL(2,R)L×SL(2,R) conformal symmetry, we show that the entropy obtained via the Cardy formula equals the standard Bekenstein-Hawking entropy, and that the cross section obtain is the same as results in CFT. We also study the information loss paradox of black hole radiation via the tunneling mechanism. When quantum effects are consideded, we show that information would not lose in the radiation, and the whole black hole evaporating process is entropy conserved. One interesting result is that after including quantum effects, the black hole would not evaporate entirely. These must be some black hole remnant at the end of the evaporation.
In this thesis, we construct the explicit solutions for the linearized massive and massless spin-2, vector and scalar modes around the AdS spacetimes in diverse dimen-sions. These modes may arise in extended gravities and super gravities with higher order curvature terms in general dimensions. Log modes in critical gravities can also be straightforwardly deduced. We analyze the properties of these modes and obain the tachyon-free condition, which is a generalization of the Breitenlohner-Freedman bound. These modes should be served as useful tools to study various properties of the gravity theories. On the other hand, we study some properties of black holes. We find the hidden conformal symmetry in a rotating black hole with 4 charges (Cvetic-Youm solution). After reveiving the SL(2,R)L×SL(2,R) conformal symmetry, we show that the entropy obtained via the Cardy formula equals the standard Bekenstein-Hawking entropy, and that the cross section obtain is the same as results in CFT. We also study the information loss paradox of black hole radiation via the tunneling mechanism. When quantum effects are consideded, we show that information would not lose in the radiation, and the whole black hole evaporating process is entropy conserved. One interesting result is that after including quantum effects, the black hole would not evaporate entirely. These must be some black hole remnant at the end of the evaporation.
引文
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