Electromagnetic instantons and asymmetric Hawking radiation of black holes

TL;DR

This paper explores how the topological structure of Abelian gauge theories around Euclidean Schwarzschild black holes leads to electromagnetic instantons that cause asymmetries in Hawking radiation, notably $CP$-violation.

Contribution

It demonstrates that non-trivial gauge configurations and the electromagnetic $ heta$-term in black hole backgrounds induce observable $CP$ asymmetries in Hawking radiation.

Findings

Electromagnetic instantons are classified by integer electric and magnetic charges.

Self-dual and anti-self-dual configurations have zero Euclidean energy and are compatible with Schwarzschild geometry.

The electromagnetic $ heta$-term sources $CP$-asymmetric Hawking radiation, observable as polarization imbalance.

Abstract

We argue that the topological structure of Abelian gauge theories, such as Maxwell electrodynamics, in the background of a Euclidean Schwarzschild black hole manifests itself through an asymmetry in Hawking radiation. In particular, the topology of the black hole manifold, characterised by a non-contractible 2-sphere and Euler characteristic $\chi = 2$, admits non-trivial gauge-field configurations. These take the form of 2-form field strengths that are closed but not exact. From a topological perspective, such configurations are classified by the second cohomology group, which is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$, and are labelled by integer electric ($n$) and magnetic ($m$) charges, $(n,m)$. Self-dual ($n = m$) and anti-self-dual ($n = -m$) dyonic configurations carry vanishing Euclidean energy and are fully compatible with the Euclidean Schwarzschild geometry. More general dyonic configurations, by contrast, are interpreted as off-shell Euclidean field configurations. Nevertheless, both classes contribute to the thermal equilibrium vacuum and to finite-temperature correlation functions in the corresponding Lorentzian framework. Furthermore, because of the non-trivial topology, the electromagnetic $\theta_{\rm EM}$-term contributes to the physical observables. In particular, it sources $CP$-asymmetric Hawking radiation, observable as an imbalance between left- and right-polarised photons in the emission spectrum. We briefly discuss some implications of this phenomenon.