2007/04/30 by Óscar J. C. Dias, Oscar J. C. Dias, Pedro J. Silva · 1 citation
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Boltzmann's entropy formula #Classical mechanics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Euclidean distance #Euclidean geometry #Formalism (music) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.77.084011
published as Phys.Rev.D77:084011,2008 · 37 pages. v3: Footnote and Reference added. Published version
arxiv created 2008/03/05 · openalex publication_date 2008/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.