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Black hole entropy — Jacob Bekenstein

1972 AD · Transmission: Global
PhysicsTheoryNorth American

In his doctoral thesis at Princeton University, under the supervision of John Wheeler, Jacob Bekenstein proposes in 1972 an idea that at the time seemed counterintuitive: black holes must possess their own thermodynamic entropy, proportional to the area of their event horizon. Bekenstein's motivation arises from a paradox: if an object with entropy falls into a black hole, that entropy seems to disappear from the observable universe, apparently violating the second law of thermodynamics, according to which total entropy can never decrease. Bekenstein resolves the paradox by proposing that the black hole itself must absorb that lost entropy, and that the area of the event horizon — which classical general relativity shows can never decrease, analogous to how entropy never decreases — is precisely the physical quantity that encodes that entropy. In his 1973 paper "Black holes and entropy" he formalizes this intuition and states the generalized second law of thermodynamics: the sum of ordinary entropy outside black holes plus the entropy of the black holes themselves never decreases. The proposal was initially received with skepticism, particularly from his own doctoral advisor Wheeler and, notably, from Stephen Hawking, who considered it physically untenable because a truly black object, emitting nothing, should have neither temperature nor, therefore, entropy in the usual thermodynamic sense. Hawking's own objection led him, while trying to mathematically refute Bekenstein, to calculate in 1974 that black holes do indeed emit thermal radiation — Hawking radiation — thereby unexpectedly confirming the physical validity of Bekenstein's proposal. The combination of both results has since constituted the Bekenstein-Hawking entropy formula, the foundational pillar of all black hole thermodynamics and one of the most valuable empirical clues currently available for the search for a quantum theory of gravity, by suggesting that area — not volume — encodes the physical information of a region of spacetime.

InstitutionPrinceton University
Historical regionUnited States
Primary sourceBekenstein, J.D. — "Black holes and entropy" Physical Review D 7 (1973): 2333-2346. DOI: 10.1103/PhysRevD.7.2333
Secondary sourceAmerican Physical Society — Einstein Prize citation (2015); Physics Today — Obituary of Jacob David Bekenstein
Original languageEnglish
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