Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity

TL;DR

This work uses $2d$ Jackiw-Teitelboim gravity to study black hole evaporation by anchoring bulk observables to boundary Schwarzian frames and integrating over Schwarzian reparametrizations. It derives quantum gravitational corrections to the Unruh heat bath, including Planckian spectra and energy fluxes, and defines a diff-invariant entangling surface to compute matter entanglement entropy. In a semiclassical evaporating setup with absorbing boundary conditions, the early-late Hawking entanglement grows without a Page curve, illustrating information loss within the semiclassical approximation and highlighting the need for a unitary quantum completion. The results illuminate how gravity modifies horizon thermodynamics and entanglement, offering a concrete, exactly solvable laboratory for evaporation physics and holographic bulk reconstruction.

Abstract

Using a definition of the bulk frame within 2d Jackiw-Teitelboim gravity, we go into the bulk from the Schwarzian boundary. Including the path integral over the Schwarzian degrees of freedom, we discuss the quantum gravitational Unruh effect and the Planckian black-body spectrum of the thermal atmosphere. We analyze matter entanglement entropy and how the entangling surface should be defined in quantum gravity. Finally, we reanalyze a semi-classical model for black hole evaporation studied in JHEP 1607, 139 (2016) and compute the entanglement between early and late Hawking radiation, illustrating information loss in the semi-classical framework.

Figures (15)

• Figure 1: Left: Local bulk fluxes of energy. Outgoing flux $T_{uu}$ and ingoing flux $T_{vv}$. Right: Bilocal boundary operation insertion at zero temperature, and the bulk injection of energy that it entails. The bulk energy densities $T_{uu}$ and $T_{vv}$ are zero before and after the injections, and non-zero but constant (in momentum space) and equal in between the ends of the bilocal. In the semi-classical regime, a fixed energy $E(\ell,t_{12})$ is injected by these operators.
• Figure 2: Blue (upper): exact energy spectral density $\omega \left\langle N_\omega \right\rangle_{\beta}$ of the Unruh radiation, computed from \ref{['exactplanck']}with $\beta=2$. Red (lower): semi-classical Planck black body spectrum of Unruh radiation, coming from \ref{['semiplanck']}.
• Figure 3: Total energy density $\frac{1}{V} \int_{0}^{+\infty}d\omega \, \omega \left\langle N_\omega \right\rangle_{\beta}$ of the Unruh radiation, as a function of $\beta$, computed by integrating \ref{['exactplanck']} (black dots). The exact energy \ref{['exUnruh']} (with $c=1$) is plotted as a blue line (top). The semi-classical energy \ref{['Enmat']} is plotted as a red line (bottom), computable by integrating \ref{['semiplanck']}. The inset shows in more detail the match at the exact level, and the approximation made by taking the semi-classical result.
• Figure 4: Left: Matter entanglement entropy obtained by dividing a Cauchy slice $\Sigma$ in two pieces. The bulk point is at $(z,t)$. Middle: Foliation independence of entanglement entropy on Cauchy slice. One can freely move the Cauchy surface within the blue regions, keeping it spacelike everywhere. Right: $z\to +\infty$ limit, where the entanglement entropy is between the interior (blue) and exterior (green) of the black hole. The full patch is the Poincaré frame. The result agrees with the thermal entropy of the CFT gas surrounding the black hole.
• Figure 5: Left: In a CFT, one can change a spatial interval (blue) into a time interval (green) using null paths, preserving information flow. Right: In a chiral (sector of a) CFT, one can move the endpoint of the interval (blue) along one of the null directions, e.g. up to the time interval (green), and preserve the information flow.