Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field

TL;DR

This paper explores how non-minimal electromagnetic-curvature couplings affect black hole shadows and photon rings, revealing distinct observational signatures that could test gravity modifications.

Contribution

It derives new black hole solutions with non-minimal couplings and analyzes their observational effects on shadows and photon rings, highlighting potential for empirical constraints.

Findings

Couplings enlarge event horizons and photon spheres.

Different couplings uniquely alter shadow sizes and ring spacings.

Black hole images confirm observational signatures within resolvable regimes.

Abstract

We investigate black holes with non-minimal couplings between the electromagnetic field and spacetime curvature, focusing on their event horizons, shadows, and photon rings. Such couplings can naturally arise from both classical effective field theories of gravity and quantum effects in curved spacetime. Starting from a general action with three independent coupling terms, we derive static and spherically symmetric black hole solutions using a series expansion method. We find that all couplings enlarge the event horizon and photon sphere, while their observational consequences differ. The coupling $F^\mu_{\ \nu}F_{\mu\rho}R^{\nu\rho}$ slightly increases the shadow size and the separation between the zeroth- and first-order photon rings, leaving higher-order spacings nearly unchanged. The coupling $F_{\mu\nu}F_{\sigma\rho}R^{\mu\nu\sigma\rho}$ significantly enlarges the shadow and the zeroth-first ring separation, but rapidly suppresses the spacing between higher-order rings. In contrast, the $F^2R$ coupling reduces the shadow size and causes the zeroth- and first-order rings to nearly coincide, leading to an enhanced brightness, while increasing the separation of higher-order rings and leaving them easier to resolve observationally. We further generate black hole images via backward ray tracing and confirm these features within the observationally resolvable regime. These findings can make observational constraints on the non-minimal couplings or might provide new evidence for the modifications to gravity caused by classical or quantum effects.