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Born-Infeld AdS Black Holes Surrounded by Perfect Fluid Dark Matter

Behzad Eslam Panah, Bilel Hamil, Manuel E. Rodrigues

Abstract

We obtain exact charged AdS black hole solutions in Einstein Lambda gravity including the effects of Born Infeld nonlinear electrodynamics and Perfect Fluid Dark Matter. The influence of the PFDM and BI parameters on the event horizon is analyzed. We compute the conserved and thermodynamic quantities and verify that they satisfy the first law of thermodynamics. Thermal stability is studied in the canonical ensemble using the heat capacity and Helmholtz free energy showing how PFDM and BI parameters affect local and global stability regions. We further investigate the thermodynamics in the extended phase space by treating the cosmological constant as thermodynamic pressure obtaining consistent conserved quantities and confirming the first law. The Ehrenfest equations are analytically verified demonstrating that the critical behavior corresponds to a second order phase transition. Heat engines associated with these black holes are also constructed to examine how PFDM and BI parameters influence their efficiency. Finally we analyze the geodesic structure through timelike and null trajectories using the effective potential determining conditions for stable and unstable circular orbits the innermost stable circular orbit and the photon sphere. PFDM significantly modifies the orbital structure while BI corrections are weaker.

Born-Infeld AdS Black Holes Surrounded by Perfect Fluid Dark Matter

Abstract

We obtain exact charged AdS black hole solutions in Einstein Lambda gravity including the effects of Born Infeld nonlinear electrodynamics and Perfect Fluid Dark Matter. The influence of the PFDM and BI parameters on the event horizon is analyzed. We compute the conserved and thermodynamic quantities and verify that they satisfy the first law of thermodynamics. Thermal stability is studied in the canonical ensemble using the heat capacity and Helmholtz free energy showing how PFDM and BI parameters affect local and global stability regions. We further investigate the thermodynamics in the extended phase space by treating the cosmological constant as thermodynamic pressure obtaining consistent conserved quantities and confirming the first law. The Ehrenfest equations are analytically verified demonstrating that the critical behavior corresponds to a second order phase transition. Heat engines associated with these black holes are also constructed to examine how PFDM and BI parameters influence their efficiency. Finally we analyze the geodesic structure through timelike and null trajectories using the effective potential determining conditions for stable and unstable circular orbits the innermost stable circular orbit and the photon sphere. PFDM significantly modifies the orbital structure while BI corrections are weaker.
Paper Structure (15 sections, 107 equations, 20 figures, 1 table)

This paper contains 15 sections, 107 equations, 20 figures, 1 table.

Table of Contents

  1. Introduction
  2. Action and Field Equations
  3. Black Hole Solutions
  4. Thermodynamic Properties in Non-Extended Phase Space
  5. Conserved and Thermodynamic Quantities
  6. Heat Capacity: Local Stability
  7. Helmholtz free energy: Global Stability
  8. Thermodynamic Properties in Extended Phase Space
  9. Classical Ehrenfest Relations
  10. Heat Engine
  11. Topological Thermodynamic Defects
  12. Timelike geodesics
  13. The effective force
  14. Null geodesics
  15. Discussion and Conclusion

Figures (20)

  • Figure 1: The mertic function $\psi(r)$ versus $r$ for different values of parameters $b$ in the left panel, and $\beta$ in the right panel.
  • Figure 2: The total mass $M$ versus $r_{+}$ for different values of $b$ (the left panel) and $\beta$ (the right panel).
  • Figure 3: The heat capacity $C$ (thick lines) and temperature $T$ (thin lines) are shown as functions of $r_{+}$ for different values of $b$ in the left panel and $\beta$ in the right panel.
  • Figure 4: The mertic function $\psi (r)$ versus $r$ for different parameters $b$ in the left panel and $\beta$ in the right panel.
  • Figure 5: $P-V$ diagram for Carnot cycle which consists two isobars (paths of $1\rightarrow 2$ and $3\rightarrow 4$) and two isochores (paths of $2\rightarrow 3$ and $4\rightarrow 1$).
  • ...and 15 more figures