Entropy of a Black Hole

We present a straightforward method to determine the entropy of a Schwarzschild black hole by analyzing the entropy associated with its Hawking radiation. Specifically, we demonstrate that when a thermodynamic system dissipates energy exclusively through blackbody radiation, the corresponding decrease in its entropy equals three-fourths of the entropy carried away by the emitted radiation. This result allows us to establish a connection between the entropy of an evaporating black hole and that of its Hawking radiation. By explicitly evaluating the total entropy of the radiation released over the complete evaporation process, we recover the Bekenstein–Hawking entropy of the original black hole. Furthermore, this study derives the relationship between black hole area entropy and information theory. The curved spacetime around a black hole can act similarly to an optical lens, forming images of objects. The maximum information that a black hole can contain is constrained by both the Compton wavelength of the infalling object and the black hole’s size. When matter enters a black hole, its detailed information is lost due to the no-hair theorem, leading to a corresponding increase in entropy. Consequently, the area law of black hole entropy suggests that Bekenstein–Hawking entropy should be interpreted as a form of information entropy rather than purely thermodynamic entropy.