Abstract: In this talk I focus on the low temperature expansion of the first law of thermodynamics for near-extremal black holes and derive "laws of extremal black hole dynamics" and show that for extremal black holes with non-vanishing entropy, the leading order contribution yields an expression for their extremal entropy in agreement with the entropy function result and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and consistent both with the presence of local AdS2 and AdS3 near horizon throats for extremal black holes and with the suggested quantum microscopic descriptions (AdS2/CFT1, Kerr/CFT and EVH/CFT).
ICTP - Strada Costiera, 11
I - 34151 Trieste Italy (+39) 040 2240 111 email@example.com