Thermodynamics of charged rotating black strings in extended phase space

Abstract: We investigate the thermodynamics of asymptotically Anti-de Sitter charged and rotating black strings in extended phase space, in which the cosmological constant is interpreted as thermodynamic pressure and the thermodynamic volume is defined as its conjugate. We find the thermodynamic volume, the internal energy, and the Smarr law. We study the thermal stability and show that some of the solutions have positive specific heat, which makes them thermodynamically stable. We find, for the first time, there is a critical point for charged solutions which occurs at the point of divergence of specific heat at constant pressure. This supports the existence of a second-order phase transition analogous to the liquid-gas critical point in Van der Waals fluids. We also study the maximal efficiency of a Penrose process and find that an extremal rotating black string can have an efficiency of up to 50%. We also find the equation of state for uncharged solutions. By comparing with the liquid-gas system, we observe that there is not a critical behavior to coincide with those of the Van der Waals system.

• The paper introduces an extended phase space formulation by treating the cosmological constant as pressure, revealing new thermodynamic variables for charged rotating black strings.
• It demonstrates thermal stability via specific heat analysis, identifying parameter regions where stable black string configurations exist.
• The study shows that extreme rotation enhances the efficiency of the Penrose process, achieving energy extraction rates up to 50% under AdS boundary conditions.

Thermodynamics of Charged Rotating Black Strings in Extended Phase Space

The study presented in this paper investigates the intriguing thermodynamic properties of charged rotating black strings within asymptotically Anti-de Sitter (AdS) spaces, particularly focusing on the extended phase space framework. This approach treats the cosmological constant as a thermodynamic pressure, enabling novel insights into black hole thermodynamics analogous to conventional thermodynamic systems. Such approaches have gained traction due to their capability to elucidate phenomena analogous to phase transitions and critical behavior known in classical thermodynamics.

The study addresses several key aspects: the definition and role of thermodynamic volume, the internal energy, the Smarr relation in extended phase space, and the thermal stability of solutions. The examination of black string configurations for various topologies offers insights into the complex landscape of black hole thermodynamics.

Key Findings

1. Thermodynamic Volume and Pressure: By interpreting the cosmological constant as a pressure term, the black string system exhibits a distinctive set of thermodynamic variables, with the thermodynamic volume being the conjugate variable. The relation is pivotal in understanding the extended Smarr relation, which integrates additional variables into the conventional law of black hole thermodynamics.
2. Thermal Stability and Specific Heat: The stability analysis reveals that certain black string solutions are thermodynamically stable, characterized by regions of positive specific heat. This points to viable, stable configurations in specific parametric regimes, which are essential for understanding the thermodynamic cycles and energy extraction mechanisms possibly viable in such cosmic objects.
3. Efficiency of the Penrose Process: The analysis of the Penrose process efficiency indicates that extremally rotating black strings can achieve efficiencies up to 50%, markedly higher compared to zero cosmological constant scenarios. This denotes the profound impact of the AdS boundary conditions on potential energy extraction mechanisms from black holes.
4. Equation of State: Results show no critical behavior akin to a liquid-gas phase transition in the examined black string systems, contrasting with Van der Waals systems. This suggests that while mathematical parallels can be drawn, the physical phenomena remain distinct.

Implications and Future Directions

The study enhances the theoretical understanding of black holes in gauged supergravity models and string theories. The application of extended thermodynamics to charged, rotating solutions is not only pivotal for theoretical advancements but may have implications for understanding the holographic duals in the context of AdS/CFT correspondence.

Future work could explore higher-dimensional extensions, where the extended phase space formulation may reveal richer structures. Moreover, incorporating nonlinear electrodynamics or higher-curvature gravity theories could provide deeper insights into black hole microstructures and aid in developing an encompassing framework for black hole chemistry.

The research herein establishes a foundational understanding of black string thermodynamics in an extended phase space, serving as a stepping stone for both theoretical refinement and potential experimental correlates in astrophysical observation of extreme gravitational entities.