New Hamiltonian constraint operator for loop quantum gravity

A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method, so that its regulated version in the kinematical Hilbert space is diffeomorphism covariant and creates new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.Comment: 5 pages; a few modification

Loop quantum black hole in a gravitational collapse model

The gravitational collapse plays an important role in the formation of black holes as well as for our understanding of the spacetime structure. In this paper, we propose the exterior effective spacetime that are well matched to the interior effective model of loop quantum cosmology for the Datt-Oppenheimer-Snyder gravitational collapse model. The analysis shows that, as the collapse goes on, the quantum-corrected black hole can form with the occurrence of horizon. The quantum gravitational effects will stop the collapse of the dust matter when the energy density reaches the Planck scale and bounce it to an expanding phase, resulting in the resolution of the singularity of the classical black hole. Moreover, the quantum gravitational corrections can affect the black hole shadows by their sizes. The stability of the quantum-corrected black hole under perturbations is also studied by calculating the quasinormal modes. It turns out that the quantum-corrected black hole is stable against the scalar and vector perturbations.Comment: 14 pages, 9 figure

Black hole image encoding quantum gravity information

The quantum extension of the Kruskal spacetime indicates the existence of a companion black hole in the universe earlier than ours. It is shown that the radiations from the companion black hole can enter its horizon, pass through the deep Planck region, and show up from the white hole in our universe. These radiations inlay extra bright rings in the image of the black hole in our universe, and some of these rings appear distinctly in the shadow region. Therefore, the image of the black hole observed by us encodes the information of quantum gravity. The positions and widths of the bright rings are predicted precisely. The predictive values for supermassive black holes are universal for a quite general class of quantum-modified spacetimes with the phenomenon of black hole to white hole transition. Thus, our result opens a new experimental window to test this phenomenon predicted by quantum gravity.Comment: 6+6 pages, 6 figures, Fig. 6 and some relevant discussions is adde