Five Problems in Quantum Gravity

Andrew Strominger

doi:10.1016/j.nuclphysbps.2009.07.049

Abstract

We present five open problems in quantum gravity which one might reasonably hope to solve in the next decade. Hints appearing in the literature are summarized for each one.

Highlights

We present five open problems in quantum gravity which one might reasonably hope to solve in the decade
Consistency with the generalized laws of thermodynamics requires that this entropy can be accounted for by counting some kind of quantum microstates
This correction can be viewed as the entanglement entropy of the quantum states of the quantum fields inside and outside the horizon

Summary

The problem

In the seventies [31] Hawking gave a very simple and beautiful argument that information is destroyed by black holes. (4) Non-local remnant: Sent(t−) grows monotonically as expected from Hawking’s analysis for a time of order M 3, and decreases back to zero over a time of order M 8/3 This is possible if, when the black hole becomes sub-Planckian, the information is stored not in a local Planck-sized region around the origin, but rather non-locally in a region of radius M 8/3: (using S ∼ (ER)3/4 and E ∼ 1 this accommodates an entropy S ∼ M 2). (ii) More hints come from thinking about the behavior of field theory two point functions at infinity in the presence of an eternal black hole [35] These correlators have a thermal exponential decay at large time separations. Interesting recent work in this direction appears in [36]