论文标题
有效的循环量子重力框架，用于真空球形对称空间时间
Effective loop quantum gravity framework for vacuum spherically symmetric space-times
论文作者
论文摘要
我们为$ \barμ$ $ $ $ \barμ$方案开发了一个由循环量子重力动机的固体校正方案，用于真空球形对称空间时间。这是通过在经典理论中施加面积量规，然后在汉密尔顿约束中以物理长度$ \ ell _ {\ rm pl} $来表达Ashtekar-Barbero连接的其余部分。可以准确找到有效的哈密顿约束的固定解决方案，我们给出了Painlevé-Gullstrand坐标中有效度量的明确形式。该解决方案具有正确的经典限制，量子重力校正在大距离上迅速衰减，并且曲率标量由普朗克尺度界定，独立于黑洞质量$ m $。此外，该解决方案对于Radii $ X \ ge X _ {\ rm min} \ sim（\ ell _ {\ el _ {\ rm pl}^2 m）^{1/3} $，指示对物质字段的需求，并指示由Planck尺度界定的能量密度，以提供空间时的曲率源。最后，对于$ m \ gg m _ {\ rm pl} $，时空具有外部且内在的地平线，其中外向径向径向null Geodesics的扩展再次成为正面。另一方面，对于足够小的$ m \ sim m _ {\ rm pl} $，有效度量中根本没有视野。
We develop an effective framework for the $\barμ$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then expressing the remaining components of the Ashtekar-Barbero connection in the Hamiltonian constraint in terms of holonomies of physical length $\ell_{\rm Pl}$. The stationary solutions to the effective Hamiltonian constraint can be found exactly, and we give the explicit form of the effective metric in Painlevé-Gullstrand coordinates. This solution has the correct classical limit, the quantum gravity corrections decay rapidly at large distances, and curvature scalars are bounded by the Planck scale, independently of the black hole mass $M$. In addition, the solution is valid for radii $x \ge x_{\rm min} \sim (\ell_{\rm Pl}^2 M)^{1/3}$ indicating the need for a matter field, with an energy density bounded by the Planck scale, to provide a source for the curvature in the space-time. Finally, for $M \gg m_{\rm Pl}$, the space-time has an outer and also an inner horizon, within which the expansion for outgoing radial null geodesics becomes positive again. On the other hand, for sufficiently small $M \sim m_{\rm Pl}$, there are no horizons at all in the effective metric.
