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The volume of a black hole under noncommutative spacetime background is foundto be infinite, in contradiction with the surface area of a black hole, or itsBekenstein-Hawking (BH) entropy, which is well-known to be finite. Our resultrules out the possibility of interpreting the entropy of a black hole bycounting the number of modes wrapped inside its surface if the finalevaporation stage can be properly treated. It implies the statisticalinterpretation for the BH entropy can be independent of the volume, providedspacetime is noncommutative. The effect of radiation back reaction is found tobe small and doesn't influence the above conclusion.

Infinite Volume of Noncommutative Black Hole Wrapped by Finite Surface