Black Hole Evaporation in Loop Quantum Gravity

TL;DR

This work surveys a mainstream Loop Quantum Gravity perspective on black hole evaporation, arguing that event horizons and singularities are replaced by quasi-local horizons and a quantum-resolved transition surface, respectively. It develops a two-stage evaporation scenario: a semi-classical regime with dynamical horizons and entangled Hawking partners, followed by a Planck-scale regime where quantum geometry cures the singularity and enables late-time purification of radiation at infinity. The approach emphasizes local, flux-driven horizon dynamics and a quantum-corrected spacetime that remains predictive through the Planck regime, offering a concrete pathway toward unitary evolution without resorting to event horizons or thunderbolt singularities. While promising, it also highlights unresolved issues in the red blob region and in full quantum gravity evolution, inviting further work with LQG techniques and comparisons with string-theoretic ideas.

Abstract

The conference \emph{Black Holes Inside and Out} marked the 50th anniversary of Hawking's seminal paper on black hole radiance. It was clear already from Hawking's analysis that a proper quantum gravity theory would be essential for a more complete understanding of the evaporation process. This task was undertaken in Loop Quantum Gravity (LQG) two decades ago and by now the literature on the subject is quite rich. The goal of this contribution is to summarize a mainstream perspective that has emerged. The intended audience is the broader gravitational physics community, rather than quantum gravity experts. Therefore, the emphasis is on conceptual issues, especially on the key features that distinguish the LQG approach, and on concrete results that underlie the paradigm that has emerged. This is \emph{not} meant to be an exhaustive review. Rather, it is a broad-brush stroke portrait of the present status. Further details can be found in the references listed.

Figures (4)

• Figure 1: (a) Left Panel: The Penrose diagram of a collapsing star, used by Hawking in his calculation in the external potential approximation. (b) Middle Panel: The Penrose diagram proposed by Hawking in 1975 to incorporate the back reaction of an evaporation black hole. (c) Right Panel: The classical Vaidya space-time depicting a null-fluid collapse.
• Figure 2: (a) Left Panel: A dynamical horizon $H$, foliated by marginally trapped surfaces. A typical leaves are marked $S_t$ and two null normals to it are denoted by $\ell^a$ and $n^a$. $\Delta H$ is the portion of the DH bounded any $S_1$ and $S_2$. (b) Middle Panel: The Penrose diagram of a classical 2-d black hole formed by the collapse of a massless scalar field coming in from $\mathscr{I}^{-}$ depicted by the shaded region. Space-time metric is flat to the past of the shaded region and represents a static black hole to the future. Again, the event horizon forms and evolves in the flat region of space-time. (c) Right Panel: The semi-classical extension of the space-time in panel (b). During the collapse, a trapping dynamical horizon T-DH (depicted in red) forms, is space-like, and grows as the matter collapses. At the end of this process, T-DH becomes time-like and starts shrinking in area due to the influx of negative energy. The shaded yellow region is semi-classical and trapped. To its future one needs full quantum gravity.
• Figure 3: (a) Left Panel: Penrose diagram of Kruskal space-time. Only region II is of interest for the issue of singularity resolution. (b) Middle Panel: The LQG extension of region II of Kruskal space-time via singularity resolution. Singularity is replaced by a regular 3-manifold $\tau$ that separates the trapped and anti-trapped regions. (c) Right Panel: A time-like 3-surface $\Sigma$ joins two MTSs (depicted by blobs), one on the Trapping horizon that constitutes the past boundary of the trapped region and the other on the Anti-Trapping horizon that constitutes the future boundary of the anti-trapped region.
• Figure 4: (a) Left Panel: The expected semi-classical space-time in LQG. Planck regime has been cut out. The DH has two branches, the expanding, space-like, left branch is formed as a result of the collapse and the contracting, time-like, right branch (that replaces the event horizon of the Panel (c) of Fig. \ref{['fig:1']}). Each branch is a T-DH . Together, they bound a trapped region. (b) Middle Panel: The conjectured full space-time of LQG. Curvature is Planck scale in the shaded pink region that contains the transition surface $\tau$. To the past of $\tau$ we have a trapped region, bounded by a T-DH and the transition surface $\tau$, and to the future of which we have an anti-trapped region, bounded by $\tau$ and an AT-DH . The well-developed approximation methods of LQG are inapplicable to the prink blob where the fluctuations of geometry could be very large. Because their influence has not been explored, the space-time portion to the future of the AT-DH is left blank. (c) Right Panel: Hawking's original Penrose diagram for an evaporating black hole is reproduced here for ready comparison with the LQG proposals.