Carlo Rovelli

The concrete perspective of using interference to measure Gravity Induced Entanglement in the lab is a very exciting development for quantum gravity. While the measurements considered so far only test the nonrelativistic regime, the same technique might allow access to genuine relativistic quantum effects. Among these, there might be the possibility of direct detection of time quantum discreteness.

There are three distinct regions where quantum gravity becomes non-negligible in a black hole spacetime.  There is a precise sense in which these three regions are causally disconnected, and therefore arguably independent.   I illustrate a number of indications we have about what happens in each of them, coming both from the classical Einstein equations and from loop quantum gravity.  These point all to an interesting scenario: long living remnants stabilized by quantum gravity, formed by a large and slowly decreasing interior enclosed into a small anti-trapping horizon.

The covariant (spinfoam) formulation of loop gravity is a tentative physical quantum theory of gravity with well defined transition amplitudes.  I give my current understanding of the state of the art in this research direction, the issues that are open and need to be explored, and the current attempts to use the theory to compute quantum effects in the early universe and in black hole physics.

The possibility of observing quantum gravitational phenomena, viewed as remote until not long ago, is increasingly considered to be plausible.  A potentially observable phenomenon is the decay of black holes via a quantum gravitational tunneling akin to standard nuclear decay.  Loop quantum gravity can be used to compute the corresponding lifetime.  This could be much shorter than the Hawking radiation time, rendering the effect astrophysically relevant.

Quantum effects render black holes unstable.  Besides Hawking radiation there is another, genuinely quantum gravitational, source of instability: the Hajicek-Kiefer explosion via tunnelling to a white hole.  A recent result in classical general relativity makes this decay channel plausible: there is an exact external solution of the Einstein equations locally (but not globally) isometric to extended Schwarzschild, which describes an object collapsing into a black hole and then exploding out of a white hole. The tunnelling time can in principle be computed using Loop Quantum Gravity.

In LQG we work in the spirit of Antonio Machado: "Traveler, there is no path; Paths are made by walking." I will present a bird's eye view of some of the paths that have emerged since Loops 11 and offer a few suggestions.

I try to make the point about what we know and what we do not yet know about the possibility of writing a quantum theory of gravity.