Narrow Results

Christodoulou and Rovelli (CR) have remarked on the large interiors possessed by static black holes. We amplify their remarks, and extend them to the spinning case.

Metrics representing black holes in General Relativity may exhibit naked singularities for certain values of their parameters. This is the case for super-extremal (J² > M > 0) Kerr and super-extremal (|Q| > M > 0) Reissner-Nördstrom spacetimes, and also for the negative mass Schwarzschild spacetime. We review our recent work where we show that these nakedly singular spacetimes are unstable under linear gravitational perturbations, a result that supports the cosmic censorship conjecture, and also that the inner stationary region beyond the inner horizon of a Kerr black hole (J² < M) is linearly unstable.

The loop quantum dynamics of Kantowski-Sachs and Bianchi-III LRS spacetimes with cosmological constant is studied in the effective spacetime description. We show that classical singularity is avoided, and replaced by bounces of the triads. Unlike the singularity resolution in other loop quantum spacetimes, evolution results in a spacetime which retains quantum curvature after the bounce on one side of the temporal evolution. In the asymptotic limit, a spacetime which is a direct product of two constant curvature spaces emerges. Interestingly, despite high curvature, the effective spacetime metric is a solution of Einstein field’s equations albeit with a different stress energy tensor. For the Kantowski-Sachs case, the resulting spacetime is a ‘charged’ Nariai spacetime, and for the Bianchi-III LRS spacetime, one obtains anti-Bertotti-Robinson spacetime with an emergent cosmological constant. The emergent ‘charge’ and cosmological constant are purely quantum geometric in origin.