| Summary: | Perfect black-body emitters in a flat three-dimensional space are characterized by the well-known relation S˙flat3D=(32π2AP3/1215ħ3)1/4, where S˙flat3D and P are respectively the entropy and energy emission rates out of the 3-D hot body, and A is the 2-D surface area of the emitting body. However, Bekenstein and Mayo have pointed out that three-dimensional Schwarzschild black holes are characterized by a qualitatively different relation: S˙BH3D=CBH3D×(P/ħ)1/2, where CBH3D is a numerically computed proportionality coefficient. Thus, in their entropy emission properties, these three-dimensional black holes effectively behave as one-dimensional entropy emitters: in particular, they respect Pendry's upper bound S˙flat1D=Cflat1D×(P/ħ)1/2 on the entropy emission rate out of one-dimensional flat-space thermal bodies, where Cflat1D=(π/3)1/2. One naturally wonders whether this intriguing property of the three-dimensional black holes is a generic feature of all D-dimensional Schwarzschild black holes? In this paper we shall show that the answer to this question (and to the question raised in the title) is ‘Yes and No’. ‘Yes’, because we shall prove that all D-dimensional Schwarzschild black holes are characterized by the one-dimensional functional relation S˙BHD=CBHD×(P/ħ)1/2. ‘No’, because we shall show that, in the large-D limit, the analytically calculated coefficients CBHD are larger than Cflat1D=(π/3)1/2, implying that higher-dimensional black holes may violate Pendry's upper bound on the entropy emission rate of one-dimensional physical systems.
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