Quantum Oppenheimer-Snyder and Swiss Cheese models

Abstract

By considering the quantum Oppenheimer-Snyder model in loop quantum cosmology, a new quantum black hole model whose metric tensor is a suitably deformed Schwarzschild one is derived. The quantum effects imply a lower bound on the mass of the black hole produced by the collapsing dust ball. For the case of larger masses where the event horizon does form, the maximal extension of the spacetime and its properties are investigated. By discussing the opposite scenario to the quantum Oppenheimer-Snyder, a quantum Swiss Cheese model is obtained with a bubble surrounded by the quantum universe. This model is analogous to black hole cosmology or fecund universes where the big bang is related to a white hole. Thus our models open a new window to cosmological phenomenology.

Black hole image encoding quantum gravity information

“…This is impossible in the classical Kruskal spacetime due to the existence of the horizon and singularity. However, the quantum extension of the spacetime indicates that the classical singularities can be resolved and there are a series of universes other than ours where companion BHs exist [17][18][19]. This provides an opportunity to observe the light signals that enter the horizon of a companion BH in the universe earlier than ours, travel through the highly quantum region, and occur in the image of the BH in our universe.…”

“…A few quantum extensions of the Kruskal spacetime have been proposed in the study of loop quantum gravity (LQG) [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. While the model in [19] will be employed in the following calculation, our analysis is applicable for all these quantum spacetimes where a BH-to-WH transition occurs. The metric of the LQG modified spherically symmetric spacetime reads…”

“…where the geometric unit with G = 1 = c is chosen such that p = √ is the Planck length and γ denotes the Barbero-Immirzi parameter [31]. This modified spacetime was derived from two independent approaches in LQG [19,32]. For realistic consideration, we assume that the BH is massive, i.e., M 4 √ α/(3 √ 3).…”

“…For realistic consideration, we assume that the BH is massive, i.e., M 4 √ α/(3 √ 3). In this case, f (r) has two real roots r ± > 0, corresponding to the two horizons in the maximally extended spacetime [19,33], whose Penrose diagram is shown in Fig. 1.…”

On the geometry of the black-to-white hole transition within a single asymptotic region

“…We match the exterior geometry to the star [9,12]. As shown in [36], the geometry of the interior of the hole outside the star is then uniquely determined by the evolution of the bouncing star and the local Killing symmetry. It turns out to be similar to the interior geometry of a Reissner-Nordström black hole.…”