Asymptotically-Flat Black Hole Solutions in Symmergent Gravity

Symmergent gravity is an emergent gravity model with an $R+R^2$ curvature sector and an extended particle sector having new particles beyond the known ones. With constant scalar curvature, asymptotically flat black hole solutions are known to have no sensitivity to the quadratic curvature term (coefficient of $R^2$). With variable scalar curvature, however, asymptotically-flat symmergent black hole solutions turn out to explicitly depend on the quadratic curvature term. In the present work, we construct asymptotically-flat symmergent black holes with variable scalar curvature and use its evaporation, shadow, and deflection angle to constrain the symmergent gravity parameters. Concerning their evaporation, we find that the new particles predicted by symmergent gravity, even if they do not interact with the known particles, can enhance the black hole evaporation rate. Concerning their shadow, we show that statistically significant symmergent effects are reached at the $2\,\sigma$ level for the observational data of the Event Horizon Telescope (EHT) on the Sagittarius A* supermassive black hole. Concerning their weak deflection angle, we reveal discernible features for the boson-fermion number differences, particularly at large impact parameters. These findings hold the potential to serve as theoretical predictions for future observations and investigations on black hole properties.