Quasiperiodic oscillations, weak field lensing and shadow cast around black holes in Symmergent gravity

In this work, we performed a systematic study of the Symmergent gravity (SG) in a black hole (BH) environment. Being an emergent gravity model in which gravity emerges to restore the gauge symmetries and stabilize the Higgs boson mass in a way giving a holographic ultraviolet (UV) completion of the underlying quantum field theory, the SG involves the general relativity (GR) plus quadratic-curvature term with a loop-induced coupling c₀ being proportional to the boson–fermion number difference. We investigated c₀ and other quantities by utilizing the various BHs observations. In this regard, we investigated particle dynamics, obtained Keplerian frequencies describing the harmonic oscillations, and determined quasi periodic oscillations (QPOs) about such orbits by using the relativistic precession (RP), warped disk (WD), and epicyclic resonant (ER) models. We also analyse the BH shadow and determine constraints on the loop parameter c₀ from the Event Horizon Telescope (EHT) data for both the static observers and observers co-moving with the cosmological expansion. We explored the weak deflection angle by considering the effect of finite distance and studied the resulting Einstein rings. We conclude the work by giving an overall discussion of the quasiperiodic oscillations, shadow cast, and weak deflection angle, with a mention of future prospects concerning other possible investigations of the SG. We also study weak deflection angle and planetary perihelion shift and determined bounds on the SG parameters. Furthermore, we compute shadow radius for both static and co-moving observers near and far from the Symmergent BH and revealed the sensitivity of these observers to the model parameters. We conclude the work by giving an overall discussion and giving future prospects concerning other possible analyses of the SG.