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The near-horizon conformal symmetry of nonextremal black holes is shown to bea mandatory ingredient for the holographic scaling of the scalar-fieldcontribution to the black hole entropy. This conformal tightness is revealed bysemiclassical first-principle scaling arguments through an analysis of themultiplicative factors in the entropy due to the radial and angular degrees offreedom associated with a scalar field. Specifically, the conformal SO(2,1)invariance of the radial degree of freedom conspires with the areaproportionality of the angular momentum sums to yield a robust holographicoutcome.

Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics