Black holes in effective loop quantum gravity: Hawking radiation

TL;DR

This work investigates Hawking radiation in black holes modeled by emergent modified gravity with holonomy corrections from loop quantum gravity. By enforcing anomaly-free constraint brackets and a covariant emergent line element, the authors show that the Hawking spectrum remains universal across minimal and nonminimal scalar couplings, with holonomy effects entering primarily through the greybody factors and the scalar potential. They compute the low-frequency greybody transmission for both constant and decreasing holonomy functions, revealing that monotone holonomy slows evaporation but does not alter thermality at leading order, and they analyze backreaction using covariant and canonical approaches to quantify energy loss and potential end-states. Overall, the paper demonstrates that EMG can yield consistent, covariant black hole thermodynamics and provides a framework to study evaporation, backreaction, and possible remnants within a semiclassical regime tied to loop quantum gravity corrections.

Abstract

Emergent modified gravity provides a covariant framework for holonomy effects in models of loop quantum gravity with consistent black hole solutions coupled to a scalar field. Several independent studies of the Hawking thermal distribution are shown here to lead to the same final result. This internal consistency is a direct consequence of general covariance, which is analogous to the situation in classical general relativity but highly nontrivial in the context of modified canonical gravity. Holonomy corrections to the evaporation rate enter through the greybody factor, slowing down the evaporation process when the holonomy modification function decreases monotonically. Accounting for backreaction, corrected covariant semi-classical stress-energy tensors are computed in various vacuum states. Thanks to these results, the new concept of a net stress-energy tensor makes it possible to compute evaporation rates directly from energy conservation laws.

Figures (4)

• Figure 1: Potential vs. radial coordinates $x$ for constant holonomy function with $\tilde{\lambda}=0.3$ and $M=1$. The potential vanishes at the horizon and flattens asymptotically.
• Figure 2: Potential as a function of the radial coordinate $x$ for decreasing holonomy function with $\Delta=1$ and $M=2$. The potential is vanishing at the horizon and flattens asymptotically.
• Figure 3: (a) Energy emission for a classical black hole represented by a black solid line ($\tilde{\lambda}=0$) and the minimally coupled constant holonomy correction by a dashed line ($\tilde{\lambda}=0.5$) and dot-dashed line $\tilde{\lambda}=0.9$. (b) The energy emission for a constant holonomy function with $\tilde{\lambda}=0.5$ for minimal coupling (solid line) and nonminimal coupling (dashed line). The nonminimal coupling implies slower rates in comparison with the minimal coupling. However, both are faster in comparison with the classical evaporation ($\tilde{\lambda}=0$).
• Figure 4: Energy flux for the classical case (solid line), the minimally coupled (dashed line), and the nonminimally coupled (dot-dashed) scalar field with a decreasing holonomy function, using $\Delta=1$. The minimum appears for both minimally and nonminimally coupled cases, with the latter evaporating more slowly and reaching a smaller value of energy extraction.