Observational appearance and photon rings of nonsingular black holes from anisotropic fluids

[EN] We consider the optical appearance of a nonsingular, spherically symmetric black hole from Eddingtoninspired Born-Infeld gravity coupled to anisotropic fluids. Such a black hole has a single (external) horizon located very near the Schwarzschild radius, rh = 2M, while its surface of unstable bound geodesics (photon sphere) is located at a moderately shortened radius than its Schwarzschild counterpart. Relying on a geometrically and optically thin accretion disk with a monochromatic emission described by suitable adaptations of standard unbound profiles previously employed in the literature, we generate images of this solution, which displays relevant modifications to the typical photon ring and central brightness depression features found in black hole images. In this sense, we fit the width of the two first photon rings in order to reconstruct the Lyapunov exponent of nearly bound geodesics characterizing the theoretical ratio of successive rings. Such an exponent is tightly attached to observational features of photon rings such as their relative intensities in time-averaged images and the time-scale of hot-spots. Our results point out that nonsingular black holes of this type are hard to distinguish from their Schwarzschild counterparts using this method alone, since the theoretical, numerical, disk-modeling, and observational uncertainties are too entangled with one another to allow a neat distinction of such an exponent. It also points to the need of incorporating dynamical settings such as hot spots or quasinormal modes from gravitational wave ringdowns as a way to circumvent such difficulties.