2026/07/17 by Sandip Dutta
#gr-qc #hep-th
We develop a comprehensive relativistic framework for geometrically thin, optically thick Shakura--Sunyaev α-viscous accretion disks around rotating Hayward regular black holes embedded in a quintessence dark energy (DE) field. The static, spherically symmetric building blocks of our spacetime are each exact solutions of the Einstein field equations, sourced respectively by the Hayward non-linear electromagnetic field and a quintessence fluid with equation-of-state parameter ω<-1/3; we combine and rotate them following standard practice for this class of models, and we are explicit throughout about the resulting metric's phenomenological status. Abandoning the stress-free inner boundary of the Novikov--Thorne--Page (NTP) model, we analytically incorporate a non-zero viscous torque \Tcal\rm in at the innermost stable circular orbit (ISCO) via the relativistic vertical epicyclic frequency \Obot(r). We prove that the bolometric efficiency η=[1-E(\rISCO)]×100 % is strictly independent of the viscosity parameter α but sensitive to both the Hayward length scale l and the DE density ρ0, establishing a rigorous two-observable degeneracy-breaking strategy. At benchmark parameters (j=0.4, l=0.5M\BH, ρ0=2×10-4), the combined geometry yields η=8.71 %, substantially above the vacuum Kerr value 7.51 % at the same spin. The viscosity correction δ\Fcal/\Fcal\rm NTP diverges at r→\rISCO+, amplified by the geometric odification of the boundary pressure: the viscosity amplification ratio rises from 0.80--4.52 % (vacuum Kerr) to 0.87--6.76 % (Hayward+DE) at α=0.1, providing a clean, monotonic observational discriminator accessible to NICER and NuSTAR, independent of the bulk spectral normalisation.