The four laws of black hole mechanics in its 50th anniversary
Tiago Fernandes  1@  
1 : GRIT, CENTRA, Instituto Superior Técnico

The four laws of black hole mechanics were formulated by Bardeen,
Carter, and Hawking during their stay in the Les Houches Summer School
on Black Holes, held in August 1972. The corresponding paper was sent
to Communications of Mathematical Physics in January 1973 and
published just after. The paper contains a proof of the zeroth and
first law of black hole mechanics, while the second law was restated
from Hawking's work of 1970, and the third law was conjectured. These
laws established general properties of stationary black holes within
general relativity. Since then, some of these laws and their proofs
have been refined and even challenged. There is of course a great
intrinsic geometric value in these laws; however, the most important
contribution in the publication was ultimately the birth of black hole
thermodynamics. Indeed, the four laws of black hole mechanics strike
an astonishing resemblance to the four laws of thermodynamics.
Nevertheless, initially the authors were reluctant to assume
equivalence. With the further contributions of Bekenstein and Hawking,
an equivalence between black hole mechanics and thermodynamics was
conjectured and then shown. In this talk, I review the four laws of
black hole mechanics and its context in this fiftieth anniversary. I
then present the influence of this seminal work on black hole
thermodynamics during these 50 years, and also show some developments
related to my own work.


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