The Black Hole Information Paradox: Thermodynamics and Hawking Radiation

Black holes represent one of the most enigmatic predictions of general relativity, yet their existence introduces profound tensions between classical and quantum physics. While traditional models suggest that black holes are eternal, Stephen Hawking’s demonstration of quantum particle emission at the event horizon implies that no black hole can survive indefinitely. This phenomenon, now known as Hawking radiation, reframes black holes as thermodynamic systems with a finite lifetime and entropy that evolves over time. In this paper, I examine the theoretical foundations of Hawking radiation within the semi-classical framework, where quantum field effects emerge against a curved spacetime background. Derivations of the Hawking temperature, entropy, and evaporation timescales are presented and applied across stellar-mass, supermassive, and primordial black holes. The calculations demonstrate that while evaporation proceeds almost imperceptibly for astrophysical black holes, primordial black holes may exhibit measurable decay signatures in the current epoch. These results underscore the principle that even the most massive gravitational entities are subject to quantum instability and ultimate decay. By analyzing the thermodynamic and quantum mechanical consequences of Hawking radiation, this work situates the information paradox as a central challenge for reconciling relativity with quantum theory, even for the universe.