Black holes as gravitational atoms

Abstract

Recently, it was argued [A. Almheiri et al., arXiv: 1207.3123, A. Almheiri et al., arXiv: 1304.6483], via a delicate thought experiment, that it is not consistent to simultaneously require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling observers encounter nothing unusual as they cross the horizon. These are the three fundamental assumptions underlying Black Hole Complementarity and the authors proposed that the most conservative resolution of the paradox is that (c) is false and the infalling observer burns up at the horizon (the horizon acts as a "firewall"). However, the firewall violates the equivalence principle and breaks the CPT invariance of quantum gravity. This led Hawking to propose recently that gravitational collapse may not end up producing event horizons, although he did not give a mechanism for how this may happen. Here we will support Hawking's conclusion in a quantum gravitational model of dust collapse. We will show that continued collapse to a singularity can only be achieved by combining two independent and entire solutions of the Wheeler–DeWitt equation. We interpret the paradox as simply forbidding such a combination. This leads naturally to a picture in which matter condenses on the apparent horizon during quantum collapse.