Euclidean analysis of the entropy functional formalism

Details Euclidean analysis of the entropy functional formalism Euclidean analysis of the entropy functional formalism

2007-04-11

arxiv.org/abs/0704.1405v3

Phys.Rev.D77:084011,2008

Physics

High Energy Physics

High Energy Physics - Theory

37 pages. v3: Footnote and Reference added. Published version

Scientific paper

10.1103/PhysRevD.77.084011

The attractor mechanism implies that the supersymmetric black hole near horizon solution is defined only in terms of the conserved charges and is therefore independent of asymptotic moduli. Starting only with the near horizon geometry, Sen's entropy functional formalism computes the entropy of an extreme black hole by means of a Legendre transformation where the electric fields are defined as conjugated variables to the electric charges. However, traditional Euclidean methods require the knowledge of the full geometry to compute the black hole thermodynamic quantities. We establish the connection between the entropy functional formalism and the standard Euclidean formalism taken at zero temperature. We find that Sen's entropy function 'f' (on-shell) matches the zero temperature limit of the Euclidean action. Moreover, Sen's near horizon angular and electric fields agree with the chemical potentials that are defined from the zero-temperature limit of the Euclidean formalism.

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