Photon Rings and Shadow Size for General Integrable Spacetimes

Abstract

According to the no-hair theorem, the unique characteristics of astrophysical black holes are their masses and spins. However, recent observations from the Event Horizon Telescope (EHT) images of M87 and Sgr A* have allowed us to place constraints on possible deviations from this theory. To interpret these observations and compare them to other near horizon scale observations, we introduce a model-agnostic framework that explores deviations while maintaining generality. We start by considering a general spherically symmetric metric, which effectively applies for a polar observer in the slow rotation limit and then follow by relaxing these constraints to axi-symmetric and stationary spacetimes. We propose a nonperturbative, nonparametric spacetime-domain characterization of shadow size and related measurements that makes explicit the nature and power (or lack thereof) of shadow-size-based constraints, and facilitates comparisons among observations and targets. Furthermore, we demonstrate that relying solely on shadow size measurements does not impose a direct limitations on the value of the gtt component of the metric. However, in the case of spherically symmetric spacetime, it can impose a constraint on the radial derivative of gtt, while a more intricate constraint arises for the axi-symmetric spacetime. Moreover, the measurement of shadows and potential future observations of multiple photon rings do not provide any valuable information concerning the ergo-region and frame-dragging in axi-symmetric spacetime.