Phase Transitions of Quintessential AdS Black Holes in M-theory/Superstring Inspired Models

Abstract

We study $d$-dimensional $AdS$ black holes surrounded by Dark Energy (DE), embedded in $D$-dimensional M-theory/superstring inspired models having $Ad{S}_d\times {\mathbb{S}}^{d+k}$ space-time with $D=2d+k$. We focus on the thermodynamic Hawking-Page phase transitions of quintessential DE black hole solutions, whose microscopical origin is linked to $N$ coincident $(d-2)$-branes supposed to live in such $(2d+k)$-dimensional models. Interpreting the cosmological constant as the number of colors $\propto N^{\frac{d-1}{2}}$, we calculate various thermodynamical quantities in terms of brane number, entropy and DE contributions. Computing the chemical potential conjugated to the number of colors in the absence of DE, we show that a generic black hole is more stable for a larger number of branes for lower dimensions $d$.In the presence of DE, we find that the DE state parameter ${\omega }_q$ should take particular values, for $(D,d,k)$ models, providing a non trivial phase transition structure.

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• Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality
• Thermodynamic and Optical Behaviors of Quintessential Hayward-AdS Black Holes
• AdS black hole thermodynamics and microstructures from $f(Q)$ gravitation
• Optical Shadows of Rotating Bardeen AdS Black Holes
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields