Information paradox and island of covariant black holes in LQG

TL;DR

The paper investigates the black hole information paradox in four-dimensional covariant loop quantum gravity by analyzing two LQG-inspired effective spacetimes distinguished by a minimal-covariance parameter $\zeta$. It combines a fixed-background calculation of Hawking radiation entropy in the Hartle–Hawking state with backreaction via greybody factors and an island-program analysis on an eternal LQG background. The results show that Solution 1 exhibits persistent linear growth of radiation entropy on a fixed geometry and an enhanced evaporation rate as $M$ decreases when $\zeta$ is nonzero, while Solution 2 slows evaporation at small $M$ and may allow a remnant or black-to-white-hole transition; islands exist in the LQG geometry, with the boundary shifted by $\zeta$, and the late-time entropy growth is suppressed, preserving unitarity. Overall, the work demonstrates that covariance-respecting LQG black holes do not share a universal late-time behavior, and the island mechanism remains robust but geometry-dependent in resolving the information paradox.

Abstract

We study information paradox of four dimensional covariant black holes inspired by loop quantum gravity (LQG) with two well motivated solutions. We first prepare the spacetime in the Hartle-Hawking state, compute the radiation entropy and recover a linear growth at late time. When considering the mass loss and incorporating greybody factors, we show that for Solution~1 the LQG parameter $ζ$ leaves temperature and Planckian factor of the spectrum unchanged but enhances the near-horizon barrier, leading to a faster evaporation rate as $M$ decreases. This behavior contrasts sharply with Solution~2, which has slow evaporation rate at small $M$ and admits a non-singular continuation suggestive of a remnant or a black-to-white-hole transition. We then apply the island prescription on the eternal background and find that quantum extremal surfaces exist in solution 1 geometries; $ζ$ primarily shifts the island boundary and suppresses the late time entropy growth, preserving unitarity. Our results highlight that covariance-respecting LQG black hole do not exhibit a universal late time behavior.

Figures (4)

• Figure 1: Penrose diagram of a spherically symmetric spacetime. The region used for the computation of radiation entropy is dotted and denoted by $R=R_{-}\cup R_{+}$.
• Figure 2: Possible late–time scenarios when the Cauchy surface intersects the minimal radius $r_\Delta$: entropy may saturate to a remnant value or decay in a white–hole transition.
• Figure 3: Effective potential $V(r)$ for different values of the LQG parameter $\zeta$ in the $l=0$ mode. A larger $\zeta$ increases the overall barrier height, affecting the greybody factor.
• Figure 4: Evaporation rates for the two cases.