Thermal phase transitions, evaporation, and shadows of regular black holes in extended gravity with stringy matter

The thermodynamics and quantum nature of black holes remain central to advancing our understanding of gravity, quantum mechanics, and high-energy physics. Motivated by the inadequacy of classical electrodynamics in extreme gravitational regimes and inspired by string theory’s prediction of extended matter structures, this work explores the rich interplay between nonlinear electrodynamics (NLED) and a surrounding cloud of strings on black hole physics. We present a novel class of regular AdS black holes within the framework of Einstein gravity, modified by both magnetic NLED sources and a cloud of strings, and perform an extensive investigation into their thermodynamic behavior, evaporation dynamics, and observational characteristics. A key motivation is to uncover whether exotic fields and high-energy corrections can alter classical predictions and stabilize black holes against evaporation. Our analysis reveals several striking results: (i) the deviation parameter $k$, magnetic charge $g$, and string cloud parameter $a$ act as regulators of black hole thermodynamics, significantly suppressing Hawking radiation and extending black hole lifetimes; (ii) Joule–Thomson expansion shows that increasing $k$ and $a$ enhances thermal stability by eliminating heating phases and broadening cooling regions; (iii) quantum gravity corrections to entropy induce richer and more complex phase transitions than those in classical models, with the HPEM thermodynamic geometry consistently identifying critical points; (iv) scalar perturbation and greybody factor analyses indicate stronger damping and reduced radiation escape under higher $k$, $a$, or $g$, suggesting suppressed quasinormal modes and observable deviations in gravitational wave signatures; and (v) the black hole shadow radius shrinks under the influence of all three parameters, opening new possibilities for observational constraints via horizon-scale imaging.