Spinfoams near a classical curvature singularity

We apply the technique of the spinfoam to study space-time, which, classically, contains a curvature singularity. We derive from the full covariant loop quantum gravity (LQG) that the region near curvature singularity has to be of the strong quantum gravity effect. We show that the spinfoam configuration describing the near-singularity region has to be of small spins $j$, in order that its contribution to the full spinfoam amplitude is nontrivial. The spinfoams in low and high-curvature regions of space-time may be viewed as in two different phases of covariant LQG. There should be a phase transition as space-time described by the spinfoam becomes more and more curved. A candidate of the order parameter is proposed for understanding the phase transition. Moreover, we also analyze the spin-spin correlation function of the spinfoam and show the correlation is of long range in the low-curvature phase. This work is a first step toward understanding the physics of black hole and early Universe from the full covariant LQG theory.

Figure 1

A Schwarzschild space-time. Region A is a sub-space-time which is far from the horizon. Region B is a sub-space-time which is inside the horizon. Region ${\mathrm{B}}^{\prime }$ is a sub-space-time which is near the quantum region of the black hole singularity.