Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity

We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4D light-cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4D Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.

Automated summary

We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action using dimensional reduction to Jackiw-Teitelboim (JT) gravity. We show that in Einstein gravity, the causal development of a region in flat Minkowski spacetime near a horizon defined by light sheets can be described by a two-dimensional dilaton theory. By relating the quantum uncertainty of horizon's spacetime position to the original 4D light-cone coordinates, we compute the uncertainty in the travel time of a photon through a causal diamond in flat 4D Minkowski space. The fluctuation in arrival time is potentially large due to both Planck and infrared scales.