Abstract
In this paper, we study the effect of dark energy on the extended thermodynamic structure and interacting microstructures of black holes in AdS, through an analysis of thermodynamic geometry. Considering various limiting cases of the novel equation of state obtained in charged rotating black holes with quintessence, and taking enthalpy H as the key potential in the extended phase space, we scrutinize the behavior of the Ruppeiner curvature scalar R in the entropy-pressure (S,P)-plane (or equivalently in the temperature-volume (T,V)-plane). Analysis of R empirically reveals that dark energy parameterized by α, significantly alters the dominant interactions of neutral, charged and slowly rotating black hole microstructures. In the Schwarzschild-AdS case: black holes smaller than a certain size continue to have attractive interactions whereas larger black holes are completely dominated by repulsive interactions which arise to due dark energy. For charged or rotating AdS black holes with quintessence, R can change sign at multiple points depending upon the relation between α and charge q or angular momentum J. In particular, above a threshold value of α, R is never negative at all, suggesting heuristically that the repulsive interactions due to quintessence are long ranged as opposed to the previously known short ranged repulsion in charged AdS black holes. A mean field interaction potential is proposed whose extrema effectively capture the points where the curvature R changes sign.
Highlights
Cosmological data points toward an accelerated expansion of our Universe due to the presence of a large negative pressure leading to the conjectured existence of an anti-gravitational force, namely dark energy [1,2,3]
We consider various limiting cases arising from the novel equation of state obtained recently in [37] and use Ruppeiner’s thermodynamic geometry to show that the inclusion of quintessence leads to novel repulsion dominated regions, modifying the behavior of microstructures of neutral, charged and rotating black holes in AdS
From the form of the equation of state given in Eq 17, it is helpful to first discuss the thermodynamic geometry of cases J 0, Q 0 and J 0, Q ≠ 0, corresponding to neutral and charged black holes in AdS, respectively surrounded by quintessence, where an exact analysis is possible
Summary
Cosmological data points toward an accelerated expansion of our Universe due to the presence of a large negative pressure leading to the conjectured existence of an anti-gravitational force, namely dark energy [1,2,3]. A novel black hole solution of charged rotating black holes in AdS in the presence of quintessence, generalizing the Kiselev’s metric was obtained by Xu and Wang [36]. For this new solution, the thermodynamics and phase transitions in the extended thermodynamic space were discussed recently giving rise to a novel equation of state [37]. We consider various limiting cases arising from the novel equation of state obtained recently in [37] and use Ruppeiner’s thermodynamic geometry to show that the inclusion of quintessence leads to novel repulsion dominated regions, modifying the behavior of microstructures of neutral, charged and rotating black holes in AdS. Some introductory discussions on thermodynamic metric structures, in the context of extended black hole thermodynamics can be found in the Supplementary Appendix
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