Entropy and gravity
James Jeffrey Binney · Entropy · 2025
Abstract The thermodynamics of self-gravitating gas confined by a spherical shell is strange: below a certain temperature its heat capacity is negative, and below an even lower temperature it can increase its entropy without limit by shrinking its core and heating the surrounding envelope. This model illustrates the physics of stars—they are balls of gas moving to states of ever higher entropy by shrinking their cores and inflating their envelopes. Adding quantum mechanics, relativity, and nuclear physics profoundly changes the later stages of the contraction: lower mass stars reach a final equilibrium, the cores of higher mass stars implode to black holes or neutron stars. Every black hole has an area that’s proportional to the square of its mass. General relativity predicts that when black holes merge the area of the final hole cannot be smaller than the sum of the areas of the progenitor holes: black-hole area, like entropy, cannot decrease. This fact suggested that a black hole has an entropy that’s proportional to its area. Quantum calculations confirmed this conjecture and supplied the constant of proportionality. A black hole also has a temperature and emits thermal radiation just like a black body with its temperature and surface area. No body can have more entropy than a black hole with the same mass. This result conflicts with the standard view that material things are excitations of the vacuum.