Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-04-10
Phys.Rev.D76:064010,2007
Physics
High Energy Physics
High Energy Physics - Theory
v3: Revtex4, 19 pages, discussion added, mistakes corrected, final version; to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.76.064010
In this paper we elaborate on the relation between the entropy formula of Wald and the "entropy function" method proposed by A. Sen. For spherically symmetric extremal black holes, it is shown that the expression of extremal black hole entropy given by A. Sen can be derived from the general entropy definition of Wald, without help of the treatment of rescaling the AdS_2 part of near horizon geometry of extremal black holes. In our procedure, we only require that the surface gravity approaches to zero, and it is easy to understand the Legendre transformation of f, the integration of Lagrangian density on the horizon, with respect to the electric charges. Since the Noether charge form can be defined in an "off-shell" form, we define a corresponding entropy function, with which one can discuss the attractor mechanism for extremal black holes with scalar fields.
Cai Rong-Gen
Cao Li-Ming
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