Entropy-Gradient Corrections to Hawking Radiation and the Formation of Stable Black Hole Remnants

Hawking radiation is conventionally formulated using quantum fields on a stationary black-hole background, producing a thermal spectrum with temperature determined by the surface gravity. Although often expressed in terms of coordinate time, the derivation itself relies only on geometric and thermodynamic relations and can be written entirely in a time-free form by parametrising evolution through the horizon entropy rather than through an external time coordinate. In this work, the horizon entropy is supplemented by a correction term that depends on an external entropy gradient associated with the local entropic environment of the black hole. This leads to an effective Hawking temperature obtained from the thermodynamic identity linking mass and total entropy. The resulting temperature differs from the standard expression whenever an entropy gradient is present at the horizon. When the entropy gradient reaches a critical value relative to the Bekenstein–Hawking entropy, the effective temperature falls to zero and evaporation terminates at a finite remnant mass. This mechanism arises within entropy-structured geometric models that are also compatible with empirical galactic dynamics, providing a regulated and thermodynamically consistent modification of Hawking evaporation without invoking ultraviolet departures from semiclassical gravity.