A textbook black hole resembles a perfectly smooth sphere: everything outside it calmly flies off to infinity. However, quantum gravity paints a different picture. Recently, within loop quantum gravity, a solution was found — a 'Kruskal' black hole where spacetime beyond the horizon behaves differently. Far from it, there is no familiar emptiness: an invisible energy seems to be spread out, preventing massive particles from escaping far. This is like a whirlpool in the ocean, where the water around it does not calm down but remains agitated at any distance.
Physicists applied to this hole a method for calculating quantum vacuum polarization — a way to measure how much the vacuum 'boils' under the influence of curvature. They numerically computed a quantity showing the activity of a scalar field outside. It turned out that the key parameter of quantum-like models (epsilon, which tracks the strength of corrections) enhances field fluctuations right at the horizon. A bit farther away, a weak negative tail appears — the field's response to the curved background, which is absent for an ordinary Schwarzschild hole.
The calculation served as a consistency check: quantum fluctuations faithfully follow local curvature without producing wild anomalies outside. This is a small but important step toward understanding how spacetime curvature and the quantum world coexist.
as written by the authors arXiv:2606.29307
A quantum macroscopic ``Kruskal'' black hole solution that incorporates quantum geometry effects has been derived in Loop Quantum Gravity as the counterpart to the classical Schwarzschild solution with a distinct imprint outside the event horizon, even at scales much larger than the Planck length. This resulting black hole quantum geometry is supported by an effective energy density of quantum origin, outside the horizon, which prevents asymptotic flatness at large distances and confines massive particles to finite radii, thereby preventing their escape to infinity. In this work we adapt to these solutions the extended Anderson-Candelas-Christensen-DeWitt approach to compute the quantum vacuum polarization in order to provide an accurate measure of the quantum activity around these black holes. We carry out a numerical implementation of the formalism and present, to our knowledge for the first time, the scalar vacuum polarization $$\langle\phi^2\rangle$$ exterior to this quantum-corrected geometry. We find that the quantum-gravity exponent $$\epsilon$$ enhances the near-horizon polarization and induces, farther out, a small negative tail that we identify -- through a parameter-free DeWitt--Schwinger comparison -- with the field's response to the nonzero curvature of the background (absent for Ricci-flat Schwarzschild). The correction scales linearly with $$\epsilon$$, the parameter tracking the quantum gravitational corrections, so that for astrophysically realistic (i.e., tiny) $$\epsilon$$, the result is numerically indistinguishable from Schwarzschild. The calculation furnishes a consistency check on the quantum activity around these solutions, the fluctuations tracking the local curvature without anomalous growth in the exterior.
The epsilon parameter in this model is so tiny for real black holes that even the most precise instruments would not notice a difference from an ordinary black hole — the effect drowns in the natural noise of the cosmos.
In Stanislaw Lem's novel 'Solaris', the planet's ocean seems to sense the presence of humans — similarly, the quantum field 'feels' the curvature of a black hole, responding even to minuscule corrections.