Black Hole Entropy: A Violation of the Second Law of Thermodynamics

According to modern theory, black holes are said to possess entropy, S_BH = k_Bc³A/4ħG, where k_B, c, ħ, and G correspond to Boltzmann’s constant, the speed of light, Planck’s constant divided by 2π, and the universal constant of gravitation, while A corresponds to the area of the event horizon. In this expression, S_BH is not extensive, as the area of the event horizon, A, the only property governing the situation, is not extensive. It is volume which is an extensive property, not area. Relative to black holes it is easy to establish that entropy is not extensive by also considering that the area of the event horizon which is given by A = 2π(R_S)², where R_S corresponds to the Schwarzschild radius. It is well accepted that R_S = 2GM/c², where M now corresponds to the mass of the black hole. As a result, black hole entropy becomes proportional and solely dependent upon M², all other terms being constants. Mass is an extensive property. However, M² is not. Extensive properties must be additive. In thermodynamics, it is essential that the entropy of large systems be extensive. To claim otherwise is a violation of the second law. As a result, black holes and their entropy cannot be reconciled with the known laws of thermodynamics.