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Paper IPM / P / 13045  


Abstract:  
Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2,\mathbbR)×U(1)^{n} (for some n) symmetry, are smooth geometries and have no event horizon, unlike black holes.
Following the ideas by R. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in the NHEG, one may associate an entropy to the NHEG, as a NoetherWald conserved charge. We work out "entropy" and "entropy perturbation" laws, which are respectively universal relations between conserved Noether charges corresponding to the NHEG and a system probing the NHEG.
We also discuss whether the laws of NHEG dynamics can be obtained from the laws of black hole thermodynamics in the extremal limit.
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