Area Functional Relation for 5D-Gauss-Bonnet-AdS Black Hole
Abstract
We present area (or entropy) functional relation for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is mass-independent whereas the entropy product relation is not mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. Smarr mass formula and first law of thermodynamics have been derived. This mass-independent relation suggests they could turn out to be an universal quantity and further helps us to understanding the nature of black hole entropy (both interior and exterior) at the microscopic level. In the Appendix, we have derived the thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with vanishing cosmological constant.
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