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Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics
The near-horizon conformal symmetry of nonextremal black holes is shown to be
a mandatory ingredient for the holographic scaling of the scalar-field
contribution to the black hole entropy. This conformal tightness is revealed by
semiclassical first-principle scaling arguments through an analysis of the
multiplicative factors in the entropy due to the radial and angular degrees of
freedom associated with a scalar field. Specifically, the conformal SO(2,1)
invariance of the radial degree of freedom conspires with the area
proportionality of the angular momentum sums to yield a robust holographic
outcome.Comment: 23 pages, 1 figure. v2 & v3: expanded explanations and proofs,
references added, typos corrected; v3: published versio