Learning Parameters of dRGT Black Holes in Nonlinear Electrodynamics with Neural Network Scenarios

Abstract

Using machine learning methods, we present constraining parameter scenarios of AdS black holes in dRGT-like massive gravity coupled to nonlinear electrodynamics. We first approach the photon sphere, the black hole shadow, and the energy emission rate with the help of high performance parallel computations. To corroborate such optical results, we develop a numerical framework to constrain the electric charge and the nonlinear electrodynamic parameter, for certain gravity regimes, via the shadow observations reported by the Even Horizon Telescope collaboration. Employing neural networks, we then examine the parameter regions of the black holes based on their consistency with EHT observations of M87$^*$, SgrA$^*_{\mathrm{VLTI}}$, and SgrA$^*_{\mathrm{Keck}}$, within the $1-σ$ and $2-σ$ confidence intervals. As a result, we find that the obtained constraints are consistent with the $SgrA^*_{\mathrm{VLTI}}$ empirical data.