https://doi.org/10.1140/epjp/s13360-024-05049-7
Regular Article
Violation of the third law of thermodynamics by black holes, Riemann zeta function and Bose gas in negative dimensions
Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia
Received:
9
May
2023
Accepted:
29
February
2024
Published online:
30
March
2024
Black holes violate the third law of thermodynamics in its standard formulation. Schwarzschild black hole entropy is inverse proportional to the square of the temperature 
and tends to infinity rather than zero when the temperature goes to zero. We search for quantum statistical models with such exotic thermodynamic behaviour. It is shown that the Schwarzschild black hole in 
spacetime dimensions corresponds to a Bose gas in a space with 
negative spatial dimensions. The Riemann zeta function is used to define the entropy of the Bose gas in negative dimension. The correspondence between black holes in higher dimensions and de Sitter space with Bose gas is considered. In particular case of 
, the corresponding Bose gas model lives in a space with 
spatial dimensions and contains a nonlocal kinetic term.
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