J.M. Bardeen (b.1939), B. Carter (b.1942) and Stephen Hawking (1942-2018).

‘The Four Laws of Black Hole Mechanics.’ Offprint from: Communications in Mathematical Physics, 31, 161-170. [Berlin:] Springer-Verlag, 1973. Provenance: the estate of the late Professor Stephen Hawking.

Fundamental paper drawing analogies between the area and surface gravity of a black hole and entropy and temperature. These are the physical properties that black holes are believed to satisfy, and are analogous to the laws of thermodynamics. Born out of an attempt to reconcile the laws of thermodynamics with the existence of black-hole event horizons, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity. Hawking radiation, whereby black holes emit thermal radiation corresponding to a certain temperature, has allowed the thermodynamic relationship between energy, temperature and entropy to be understood.

When this paper was written, it was not possible to calculate black-hole entropy based on statistical mechanics. However, in 1995, Andrew Strominger and Cumrun Vafa calculated the entropy of a supersymmetric black hole in string theory, using methods based on D-branes and string duality. Numerous subsequent calculations have confirmed their result, in turn confirming the four laws stated here for the first time.

Octavo (232 x 155mm). Stapled self-wrappers (punch holes).

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