The compressibility of rotating black holes in D-dimensions

Understand

Treating the cosmological constant as a pressure, in the context of black hole thermodynamics, a thermodynamic volume for the black hole can be defined as being the thermodynamic variable conjugate to the pressure, in the sense of a Legendre transform.

• The thermodynamic volume is explicitly calculated, as the Legendre transform of the pressure in the enthalpy for a rotating asymptotically anti-de Sitter Myers-Perry black hole in D space-time dimensions.
• The volume obtained is shown to agree with previous calculations using the Smarr relation.
• The compressibility is calculated and shown to be non-negative and bounded.