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Lower-dimensional Gauss-Bonnet gravity black holes with quintessence

G. Alencar, T. M. Crispim, J. Macedo, C. R. Muniz

Abstract

In this paper, we study the $D\to3$ 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 $ω_q$, 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 ($ω_q < -1$). Thermodynamically, the system is stable, since the specific heat is positive, and with evaporation it evolves to stable remnants whose characteristic size decreases as $ω_q$ increases, with complete evaporation prevented by quintessence effects. Furthermore, we find that all physical quantities intrinsically depend on the parameter $α$ 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.

Lower-dimensional Gauss-Bonnet gravity black holes with quintessence

Abstract

In this paper, we study the 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 , 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 (). Thermodynamically, the system is stable, since the specific heat is positive, and with evaporation it evolves to stable remnants whose characteristic size decreases as increases, with complete evaporation prevented by quintessence effects. Furthermore, we find that all physical quantities intrinsically depend on the parameter 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.
Paper Structure (7 sections, 38 equations, 7 figures)

This paper contains 7 sections, 38 equations, 7 figures.

Table of Contents

  1. Introduction
  2. BTZ Sourced by quintessence
  3. Revisiting the Gauss–Bonnet BTZ black hole
  4. The case with source
  5. Geodesic circular orbits
  6. Thermodynamics
  7. Conclusion

Figures (7)

  • Figure 1: Effective cosmological constant (top panel) and effective mass (bottom panel) as a function of the GB parameter. The parameter setting is: $\ell=2.5$ and $m_{BTZ}=1$, in Planck units.
  • Figure 2: Approximate Ricci scalar for $r$ near the origin as a function of the radial coordinate, for the singular case (top panel, $\omega = -2/5$) and regular case (bottom panel, $\omega = -5/2$) varying $\alpha$. The parameter settings are:$\ell=2.5$, in Planck units.
  • Figure 3: Metric coefficient as a function of the radial coordinate, $r$. The parameter settings are: $\alpha=-0.2$, $q=0.5$, $M=2.0$, and $\ell=2.5$, in Planck units, varying $\omega_q$
  • Figure 4: Effective potential as a function of the radial coordinate, $r$, for photons around the 3-dimensional GB black hole. The parameter settings are $\alpha=-0.2$, $q=0.5$, $M=2.0$, $\lambda=1.0$ and $\ell=2.5$, in Planck units, and varying $\omega_q$.
  • Figure 5: Hawking temperature as a function of $r_h$, fixing $q = 0.5$, $\alpha=-0.2$,$\ell = 2.5$ and varying $\omega_q$.
  • ...and 2 more figures