Euclidean analysis of the entropy functional formalism
Euclidean analysis of the entropy functional formalism
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.
Dias, Oscar J.C.
f01a8d9b-9597-4c32-9226-53a6e5500a54
Silva, Pedro J.
e1c1ac82-4d3d-47c3-bc38-06c4e704649b
15 April 2008
Dias, Oscar J.C.
f01a8d9b-9597-4c32-9226-53a6e5500a54
Silva, Pedro J.
e1c1ac82-4d3d-47c3-bc38-06c4e704649b
Dias, Oscar J.C. and Silva, Pedro J.
(2008)
Euclidean analysis of the entropy functional formalism.
Phys.Rev.D, 77, [084011].
(doi:10.1103/PhysRevD.77.084011).
Abstract
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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e-pub ahead of print date: 14 April 2008
Published date: 15 April 2008
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©2008 American Physical Society
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Local EPrints ID: 467696
URI: http://eprints.soton.ac.uk/id/eprint/467696
PURE UUID: 68022ed9-3d27-4b84-9023-c23ce659110c
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Date deposited: 19 Jul 2022 16:53
Last modified: 17 Mar 2024 03:35
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Author:
Pedro J. Silva
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