Hawking radiation and interacting fields

TL;DR

This paper investigates how interactions in scalar fields behave near black hole horizons, showing that interactions effectively switch off, which impacts Hawking radiation and raises questions about the Standard Model's behavior in such extreme environments.

Contribution

It demonstrates that scalar field interactions diminish near black hole horizons, confirming the Leahy-Unruh effect for Kerr geometries, and introduces a technique to analyze strong coupling effects close to the horizon.

Findings

Interactions vanish near the horizon, confirming Leahy-Unruh effect.

Hawking radiation can be derived using free-field techniques near the horizon.

Potential restoration of electroweak symmetry near black hole horizons.

Abstract

Hawking radiation is generally derived using a non-interacting field theory. Some time ago, Leahy and Unruh showed that, in two dimensions with a Schwarzschild geometry, a scalar field theory with a quartic interaction gets the coupling switched off near the horizon of the black hole. This would imply that interaction has no effect on Hawking radiation and free theory for particles can be used. Recently, a set of exact classical solutions for the quartic scalar field theory has been obtained. These solutions display a massive dispersion relation even if the starting theory is massless. When one considers the corresponding quantum field theory, this mass gap becomes a tower of massive excitations and, at the leading order, the theory is trivial. We apply these results to Hawking radiation for a Kerr geometry and prove that the Leahy-Unruh effect is at work. Approaching the horizon the scalar field theory has the mass gap going to zero. We devise a technique to study the interacting scalar theory very near the horizon increasing the coupling. As these solutions are represented by a Fourier series of plane waves, Hawking radiation can be immediately obtained with well-known techniques. These results open a question about the behavior of the Standard Model of particles very near the horizon of a black hole where the interactions turn out to be switched off and the electroweak symmetry could be restored.