论文标题
改进的环路 - Quantum-gravity黑洞和Nariai极限的有效动力学
Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
论文作者
论文摘要
我们提出了一个新模型的球形对称量子黑洞在还原的相空间公式中。我们通过与提供材料坐标的高斯灰尘耦合来将重力拆卸。灰尘坐标的叶子覆盖了黑洞的内部和外部。在降低球形对称性之后，我们的模型是一个1+1维场理论，其中包含无限的自由度。量子黑洞的有效动力学是由改进的物理哈密顿$ {\ bf h}_δ$生成的，其中$ \barμ$ -scheme -scheme-scheme正则化和普兰克面积尺度$Δ$实现了自动校正。有效的动力学恢复了低弯曲机制下的半经典Schwarzschild几何形状，并用Planckian曲率解析了黑洞的奇异性。我们的模型预测，黑洞在很晚时的演变达到了带电的Nariai几何形状$ {\ rm ds} _2 \ times s^2 $带有Planckian Radii。 Nariai几何形状在线性扰动下是稳定的，但可能因非扰动量子效应而不稳定。我们的模型表明，Nariai几何形状的量子隧穿以及黑洞到白孔跃迁的情况。在过渡期间，线性扰动与Lyapunov指数$λ=2πt_ {\ rm ds} \simδ^{ - 1/2} $与Hawking温度$ t _ {\ rm ds} $ $ ds $ ds} $ ds _2 $。此外，我们模型中的Nariai几何形状提供了一个有趣的示例，说明了Wheeler的金袋，并包含无限的许多红外软模式，其能量密度为零。这些红外模式跨越了希尔伯特空间，其表示1维空间差异（或witt/virasoro代数），它们是$ {\ bf h}_δ$的有效动力学的保守电荷。
We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_Δ$ where the holonomy correction is implemented by the $\barμ$-scheme regularization with a Planckian area scale $Δ$. The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition. During the transition, the linear perturbations exhibit chaotic dynamics with Lyapunov exponent $λ=2πT_{\rm dS}\sim Δ^{-1/2}$ relating to the Hawking temperature $T_{\rm dS}$ of ${\rm dS}_2$. In addition, the Nariai geometry in our model provides an interesting example of Wheeler's bag of gold and contains infinitely many infrared soft modes with zero energy density. These infrared modes span a Hilbert space carrying a representation of 1-dimensional spatial diffeomorphisms (or the Witt/Virasoro algebra) which are conserved charges of the effective dynamics by ${\bf H}_Δ$.
