Black hole chemistry: thermodynamics with Lambda

Abstract: We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequality - an inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.

• The paper presents an extended phase space where the black hole mass is interpreted as enthalpy, incorporating pressure-volume terms.
• It demonstrates phase transitions similar to those in classical fluids, including reentrant behaviors and triple points.
• The study tests the reverse isoperimetric inequality, highlighting conditions that may lead to super-entropic black holes.

Overview of "Black hole chemistry: thermodynamics with Lambda"

The paper "Black hole chemistry: thermodynamics with Lambda" by David Kubizňák, Robert B. Mann, and Mae Teo provides a detailed examination of the thermodynamic properties of black holes in the context of an extended phase space. In this analysis, the cosmological constant $\Lambda$ is treated as a thermodynamic variable, akin to pressure in classical thermodynamics, thereby enriching the thermodynamic description of black holes by introducing additional concepts such as thermodynamic volume and chemical enthalpy.

Key Concepts

• Extended Phase Space: In traditional black hole thermodynamics, the mass of a black hole is typically seen as its internal energy. However, in this extended framework, the mass is conceptualized as enthalpy, leading to the inclusion of pressure-volume (P-V) terms in the thermodynamic equations. This allows for novel interpretations of black hole thermodynamic behavior analogous to classical chemical systems.
• Thermodynamic Volume and Reverse Isoperimetric Inequality: The introduction of a thermodynamic volume for black holes adds an additional layer of complexity to black hole thermodynamics. This volume is hypothesized to satisfy the reverse isoperimetric inequality, which conjectures that for fixed thermodynamic volume, the entropy is maximized for the Schwarzschild-AdS spacetime. The paper addresses conditions under which this inequality holds and explores scenarios where it might be violated.
• Phase Transitions and Black Hole Chemistry: The paper draws parallels between black holes and chemical systems. Black holes can undergo phase transitions similar to those of Van der Waals fluids, with critical points and behaviors that mirror phenomena such as reentrant phase transitions and triple points. This analogy provides insights into black hole thermodynamic stability and transitions.

Numerical Results and Bold Claims

The authors provide several numerical results that are pivotal for understanding the thermodynamic behavior of black holes when the cosmological constant is treated as a pressure. Notable examples include the precise conditions for the existence of phase transitions analogous to those of classical fluids and the identification of possible violations of the reverse isoperimetric inequality in certain exotic black hole solutions, termed super-entropic black holes.

Implications and Future Direction

The reinterpretation of the cosmological constant as thermodynamic pressure opens numerous avenues in both theoretical and practical domains. Theoretical implications include a deeper understanding of the interplay between black hole physics and information entropy. On a practical level, it offers potential insights into the holographic principle and its relation to the thermodynamic behavior of quantum gravity systems.

Given these developments, future research might explore the extension of these thermodynamic principles to other forms of modified gravity or involve more complex interactions between matter fields and the gravitational landscape. Furthermore, the implications for AdS/CFT correspondence and our understanding of quantum gravity merit significant attention, as they may yield new insights into the fundamental structure of spacetime and gravitational interactions.

In closing, this paper signals a significant step in the direction of a richer, more nuanced understanding of black hole thermodynamics by bridging concepts from gravitational physics and chemical thermodynamics, thereby redefining how we interpret cosmological constants within the context of black hole systems.