Challenging General Relativity: Black Hole Thermodynamics

I begin with Einstein’s views on the Second Law, particularly his analogy of the perpetuum mobile of the second kind (closely related to Maxwell’s Demon). He viewed thermodynamics as a principle theory akin to his theory of relativity. The next topic is black hole thermodynamics. Stephen Hawking introduced the idea of the area law. John Wheeler posed a paradox to Jacob Bekenstein, which led to the realization that black holes have entropy. However, thought experiments soon revealed challenges, pushing Bekenstein to propose the generalized second law of thermodynamics (GSL). A major problem arose: a black hole cannot stay in equilibrium with black body radiation at any non-zero temperature. It can absorb radiation but cannot emit it, leading to a violation of the GSL. Bekenstein tried to save his theory with ad hoc explanations, but Hawking, dissatisfied with these solutions, offered a groundbreaking idea: black holes emit radiation. Using a semi-classical approach, along with principles from quantum field theory and general relativity, Hawking discovered what we now call Hawking radiation. Yet, instead of resolving all disputes, this discovery sparked even more questions. The field is far from settled, as the infamous information paradox continues to challenge our understanding (as discussed in Chap. 5).