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Black holes violate the third law of thermodynamics in its standardformulation. Schwarzschild black hole entropy is inverse proportional to thesquare of the temperature $S=1/(16 \pi T^2) $ and tends to infinity rather thanzero when the temperature goes to zero. We search for quantum statisticalmodels with such exotic thermodynamic behaviour. It is shown that theSchwarzschild black hole in $D=4 $ spacetime dimensions corresponds to a Bosegas in a space with $d=-\, 4$ negative spatial dimensions. The Riemann zetafunction is used to define the entropy of the Bose gas in negative dimension.The correspondence between black holes in higher dimensions and de Sitterspacetime with Bose gases is considered.

Violation of the Third Law of Thermodynamics by Black Holes, Riemann Zeta Function and Bose Gas in Negative Dimensions