论文标题
协变量$ {\barμ} $ - 方案有效动力学，模拟重力和非单明性黑洞：用于球形对称量子重力和CGHS模型的应用
Covariant ${\barμ}$-scheme effective dynamics, mimetic gravity, and non-singular black holes: Applications to spherical symmetric quantum gravity and CGHS model
论文作者
论文摘要
我们提出了一个新的$ \barμ$ -Scheme Hamiltonian在环形量子重力（LQG）的球形对称扇区中的有效动力学。有效的动力学通常是源自协方差拉格朗日的协变量。拉格朗日人属于4个维度的扩展模拟重力拉格朗日人的类别。我们将有效的动力学应用于宇宙学和黑洞。有效的动力学再现了非单明环 - 量子化学（LQC）的有效动力学。从有效的动力学中，我们获得了非单明的黑洞溶液，除球形对称性外，它具有杀伤对称性，并在无穷大附近渐近地降低了Schwarzschild几何形状。黑洞时空解决了经典的奇异性，并渐近地接近nariai几何$ \ mathrm {ds} _2 \ times s^2 $在黑洞内部的未来无穷大。由此产生的黑洞时空具有完整的未来null Infinity $ \ Mathscr {i}^+$。得益于一般的协方差，有效的动力学可以在轻度尺度上进行重新制定。我们将协变量$ \barμ$ -Scheme的有效动力学推广到Callan-Giddings-Harvey-Strominger（CGHS）模型，并将轻锥配方应用于带有空壳倒塌的CGHS黑洞溶液。我们专注于沿空外壳投射的有效动力。结果表明，与CGHS模型中的差异相比，2D标量曲率和Dilaton场的衍生物都是有限的。
We propose a new $\barμ$-scheme Hamiltonian effective dynamics in the spherical symmetric sector of Loop Quantum Gravity (LQG). The effective dynamics is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in 4 dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the non-singular Loop-Quantum-Cosmology (LQC) effective dynamics. From the effective dynamics, we obtain the non-singular black hole solution, which has a killing symmetry in addition to the spherical symmetry and reduces to the Schwarzschild geometry asymptotically near the infinity. The black hole spacetime resolves the classical singularity and approaches asymptotically the Nariai geometry $\mathrm{dS}_2\times S^2$ at the future infinity in the interior of the black hole. The resulting black hole spacetime has the complete future null infinity $\mathscr{I}^+$. Thanks to the general covariance, the effective dynamics can be reformulated in the light-cone gauge. We generalize the covariant $\barμ$-scheme effective dynamics to the Callan-Giddings-Harvey-Strominger (CGHS) model and apply the light-cone formulation to the CGHS black hole solution with the null-shell collapse. We focus on the effective dynamics projected along the null shell. The result shows that both the 2d scalar curvature and the derivative of dilaton field are finite, in contrast to the divergence in the CGHS model.
