BekensteinHawking

Bekenstein-Hawking entropy, commonly denoted S_BH, is the thermodynamic entropy associated with a black hole. It embodies the idea that black holes have physical entropy and that their entropy is determined by the area of the event horizon. The concept merges Jacob Bekenstein's insight that black holes must carry entropy to satisfy the second law of thermodynamics with Stephen Hawking's demonstration that black holes emit quantum radiation and have a well-defined temperature.

Formula: S_BH = k_B A c^3 / (4 G ħ), where A is the area of the event horizon, k_B is Boltzmann's constant, G is Newton's gravitational constant, ħ is reduced Planck's constant, and c is the speed of light. In natural units, S_BH = A/(4 l_P^2), with l_P the Planck length. For a Schwarzschild black hole of mass M, A = 16π G^2 M^2 / c^4, giving S_BH = 4π k_B G M^2 /(ħ c).

Implications: The entropy scales with horizon area, not volume, hinting at a fundamental limit on information storage and contributing to the holographic principle. The large entropy associated with black holes also connects gravity, quantum theory, and thermodynamics, and it plays a central role in discussions of the black hole information paradox and quantum gravity. The Bekenstein bound, a related concept, places a universal upper limit on the entropy of any system of given energy and size, reinforcing the link between information and geometry.