Testing the Kerr Paradigm via Synchrotron Radiation

General relativity has been tested in weak field regimes, but strong gravity regimes are still to be verified. The strong gravity regime with synchrotron radiation has not yet been explored. The nonthermal synchrotron emission traces the magnetic field and cosmic-ray electrons. This paper presents a test of a strong gravity regime using synchrotron radiation with two different spacetime metrics: Kerr and Cardoso, Pani, and Rico (CPR). We investigate the effects of variation in model parameters such as the spin, inclination angle, magnetic field, and nonthermal spectral index of the synchrotron radiation on flux density as a function of frequency as an observable, first in the Kerr and then in the CPR spacetime. We generate mock data observations and fit the model using Bayesian inference for both spacetimes. Assuming a uniform prior, analyzed synchrotron radiation with a Bayesian approach can distinguish Kerr and CPR spacetimes by constraining spin and deformation parameters. A Gaussian prior also allows for this distinction. However, if a Gaussian prior is used for the spin while keeping the deformation parameters uniform, only the spin can be constrained, making it impossible to differentiate between Kerr and CPR spacetime.