Black Hole Chemistry (1404.2126v1)

Abstract: The mass of a black hole has traditionally been identified with its energy. We describe a new perspective on black hole thermodynamics, one that identifies the mass of a black hole with chemical enthalpy, and the cosmological constant as thermodynamic pressure. This leads to an understanding of black holes from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. Both charged and rotating black holes exhibit novel chemical-type phase behaviour, hitherto unseen.

• The paper reinterprets black hole thermodynamics by treating the cosmological constant as pressure, defining mass as enthalpy in a new framework.
• This approach reveals that charged and rotating black holes exhibit phase transitions analogous to those seen in Van der Waals fluids.
• Further analysis shows complex behaviors like reentrant phase transitions and triple points, offering new insights into quantum gravity and gauge-gravity duality.

Black Hole Chemistry: A Thermodynamic Perspective

The paper "Black Hole Chemistry" by D. Kubiz\v{n}ak and R. B. Mann provides a compelling reinterpretation of black hole thermodynamics, expanding the conventional framework by incorporating the cosmological constant as a thermodynamic variable. This approach enables an extensive comparison between black hole systems and chemical systems, unveiling complex phase behaviors akin to those seen in standard fluids.

Conceptual Framework

The authors propose interpreting the mass of a black hole as its chemical enthalpy and associating the cosmological constant $\Lambda$ with thermodynamic pressure $P$. This modification of conventional black hole thermodynamics takes inspiration from the Smarr relation and Euler's scaling arguments, yielding a framework where black holes exhibit analogs to traditional thermodynamic properties:

• Mass $M$ is analogous to enthalpy $H$.
• Surface gravity $\kappa$ corresponds to temperature $T$.
• Horizon area $A$ resembles entropy $S$.
• Cosmological constant $\Lambda$ is proportional to $-8\pi P$.

These parallels lead to a modified first law of black hole thermodynamics, where $dM = TdS + VdP + \ldots$. Here, $V$ is the thermodynamic volume, defined as the conjugate to $P$.

Novel Phase Behaviors

This conceptual shift reveals that charged and rotating black holes exhibit phase behaviors similar to those observed in Van der Waals fluids. Specifically, the paper highlights:

1. Van der Waals-like Behavior: Charged Reissner-Nordström-AdS black holes exhibit analogs to liquid-gas phase transitions characterized by a critical point and following Maxwell's equal area law, with the criticality expression $\frac{P_c v_c}{T_c} = \frac{3}{8}$.
2. Reentrant Phase Transitions: In higher dimensions, singly-spinning Kerr-AdS black holes display reentrant phase transitions, a phenomenon typically associated with complex fluid systems. This involves a sequence of large-small-large black hole transitions as temperature varies over a specific pressure range.
3. Triple Points: Introducing two rotation parameters into the Kerr-AdS metric reveals triple point behavior, where three distinct phases of black holes can coexist, similar to the solid-liquid-gas phase diagram of classical systems.

Theoretical and Practical Implications

The introduction of a variable pressure enriches our understanding of black hole thermodynamics and opens new pathways for research in theoretical physics:

• Quantum Gravity: Reformulating black hole thermodynamics might provide deeper insights into the elusive nature of quantum gravity by revealing conditions resembling those in molecular systems.
• Gauge-Gravity Duality: These findings could influence our comprehension of the AdS/CFT correspondence, particularly in understanding dualities between thermal phases in black hole systems and phase transitions in conformal field theories.
• Extended Thermodynamic Parameters: Defining the thermodynamic volume and compressibility in this context offers potential to explore stability and dynamics in black holes, with the reverse isoperimetric inequality providing constraints reminiscent of Penrose inequalities.

Future Directions

As the exploration of black hole chemistry progresses, several directions merit further investigation:

• Analyzing Other Black Hole Metrics: Expanding this chemical analogy to other black hole solutions could uncover further exotic phase behaviors or confirm universality across different metrics.
• Quantum Mechanical Effects: Quantum corrections to thermodynamic quantities may provide a more accurate picture, potentially affecting phase transitions and the stability landscape.
• Cosmological Implications: The understanding of vacuum energy might be advanced by incorporating dynamic cosmological constants in this model.

This paper establishes a novel method for examining black holes through a thermodynamic lens conventionally used in chemical systems, thus offering fresh perspectives and raising intriguing theoretical possibilities pivotal for advancing the understanding of complex astrophysical phenomena.