Lower-dimensional Gauss-Bonnet gravity black holes with quintessence

Abstract

In this paper, we study the $D\to 3$ limit of Gauss-Bonnet gravity with quintessential matter, obtaining exact solutions that extend the BTZ metric through higher-curvature terms and quintessence coupling. The solutions exhibit a single event horizon whose radius decreases with increasing quintessence parameter ${\omega }_q$, while developing a curvature singularity at the origin for non-vanishing quintessence. The geodesic analysis reveals stable circular photon orbits exist exclusively for phantom-like quintessence (${\omega }_q<-1$). Thermodynamically, the system is stable, since the specific heat is positive, and with evaporation it evolves to stable remnants whose characteristic size decreases as ${\omega }_q$ increases, with complete evaporation prevented by quintessence effects. Furthermore, we find that all physical quantities intrinsically depend on the parameter $\alpha$ of the Gauss-Bonnet extension.These results demonstrate the profound influence of quintessential matter on both geometric and thermodynamic properties of (2+1)-dimensional black holes, offering new perspectives on gravitational theories in lower dimensions and black hole final states.

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