Sagittarius A* near-infrared flare polarization as a probe of space-time. I. Nonrotating exotic compact objects

The center of our Galaxy hosts Sagittarius A*, which is a supermassive compact object of ∼ 4.3 10^6 solar masses and is usually associated with a black hole. Nevertheless, black holes possess a central singularity that is considered unphysical, and an event horizon that leads to loss of unitarity in a quantum description of the system. To address these theoretical inconsistencies, alternative models, collectively known as exotic compact objects, have been proposed. We investigate the potential detectability of signatures associated with nonrotating exotic compact objects (ECOs) within the dataset of Sgr A* polarized flares as observed through GRAVITY and the upcoming GRAVITY+. We examined a total of eight distinct metrics that originate from four different categories of static and spherically symmetric compact objects: black holes, boson stars, fluid spheres, and gravastars. Our approach involved using a toy model that orbits the compact object in the equatorial plane at the Schwarzschild-Keplerian velocity. Using simulated astrometric and polarimetric data with current GRAVITY uncertainties as well as improved flux uncertainties expected for the GRAVITY+ upgrade, we fit the datasets across all metrics we examined. We evaluated the detectability of the metric for each dataset based on the resulting ̧hi^2_ and Bayesian information criteria-based Bayes factors. Plunge-through images of ECOs affect polarization and astrometry in a distinguishable way from the spin of a Kerr black hole. With GRAVITY's current uncertainties, none of the metrics models are discernible. However, when the data are modeled within a compact boson star background, the corresponding best fit is sufficiently superior to the Kerr fit to rule out the latter. We examined the best expected enhanced flux uncertainties and discovered that a fourfold increase in flux sensitivity enables the detection of some of the exotic compact object models we investigated. The signals of the others are too close to each other to be distinguishable. However, with the GRAVITY+ flux uncertainties, when the data are produced using an ECO model, the best-fit ECO model is significantly preferred (with a BIC-based Bayes factor exceeding two) over the best fit in the Kerr metric, such that the latter can be ruled out. Nevertheless, enhancing the astrophysical complexity of the hot-spot model might diminishes these outcomes. With the improved sensitivity of GRAVITY+, we expect to be able to determine whether Sgr A* is a Kerr black hole or some form of exotic compact object, although we will not be able to identify the specific ECO models that describe Sgr A* best.