宇称违反引力理论中的黑洞微扰
Black hole perturbation in parity violating gravitational theories
摘要：
本文研究了拉格朗日量依赖于Ricci标量和宇称违反Chern-Simons项的引力理论在静态球对称时空中的线性扰动。通过一个显式的构造，我们证明了扰动变量的哈密顿量一般从下面是没有界的，这表明这样的背景时空对扰动是不稳定的。这对违反宇称的唯象引力模型给出了一个强限制。我们还提供了一个必要和充分条件的理论属于一个特殊的类，其中没有这样的不稳定性发生。对于这样的理论，$\ell \ge 2$的传播模式的数量是三个，一个来自奇数，另外两个来自偶数。与$f(R)$理论不同的是，这些模式是相互耦合的，这可以作为一个区别性的特征来检验来自观测的宇称违反理论。所有的模式都以光速传播。无鬼条件和无快子条件与$f(R)$理论相同。对于偶极微扰，奇模和偶模完全解耦。奇模给出了一个缓慢旋转的BH解，其度规在其角动量中线性化。我们提供了这样的解决方案的积分表达式。另一方面，偶模以光速传播。对于偶模微扰，除了只移动背景BH质量的模外，还有一个以光速传播的偶模。
英文摘要：
We study linear perturbations around the static and spherically symmetric spacetime for the gravitational theories whose Lagrangian depends on Ricci scalar and the parity violating Chern-Simons term. By an explicit construction, we show that Hamiltonian for the perturbation variables is not bounded from below in general, suggesting that such a background spacetime is unstable against perturbations. This gives a strong limit on a phenomenological gravitational model which violates parity. We also provide a necessary and sufficient condition for the theory to belong to a special class in which no such instability occurs. For such theories, the number of propagating modes for $\ell \ge 2$ is three, one from the odd and the other two from the even. Unlike in the case of $f(R)$ theories, those modes are coupled each other, which can be used as a distinctive feature to test the parity violating theories from observations. All the modes propagate at the speed of light. No-ghost condition and no-tachyon condition are the same as those in $f(R)$ theories. For the dipole perturbations, the odd and the even modes completely decouple. The odd mode gives a slowly-rotating BH solution whose metric is linearized in its angular momentum. We provide an integral expression of such a solution. On the other hand, the even mode propagates at the speed of light. For the monopole perturbation, in addition to a mode which just shifts the mass of the background BH, there is also one even mode that propagates at the speed of light.
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