Thermodynamical Aspects of Gravity: New insights (0911.5004v2)

Abstract: The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, Sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In Section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In Section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in Section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.

• The paper demonstrates that gravitational field equations on horizons transform into thermodynamic identities linking geometry with entropy.
• The paper reveals that surface terms in gravitational actions correlate with horizon entropy, suggesting holographic properties in gravity.
• The paper proposes that viewing spacetime as an emergent thermodynamic system provides novel insights into quantum gravity and the cosmological constant problem.

Thermodynamical Aspects of Gravity: New Insights

The paper by T. Padmanabhan explores the intricate relationship between thermodynamics, quantum theory, and gravity. Through a detailed examination of these connections, the paper aims to provide insights into the nature of horizons as both thermodynamic and geometric entities.

At the core of this examination is the idea that horizons, such as those associated with black holes, possess thermodynamic properties, including temperature and entropy. This connection between horizons and thermodynamics suggests a deeper link to quantum gravity. The paper emphasizes that understanding this link may offer clues about the fundamental structure of spacetime.

Key discussions in the paper involve the following:

1. Geometrical Features of Horizons: The initial sections delve into the geometric nature of bifurcation horizons, characterized as surfaces where certain metric components vanish. Through the lens of different metric models, such as Schwarzschild and Rindler coordinates, the paper outlines how coordinates that become pathological at the horizon can be transformed to reveal well-behaved geometries.
2. Thermodynamic Interpretation of Gravitational Dynamics: A significant portion of the paper discusses how gravitational field equations, when evaluated on horizons, transform into thermodynamic identities—the laws of black hole dynamics paralleling those of classical thermodynamics. This symmetry between gravitational dynamics and thermodynamic concepts suggests an inherent thermodynamic nature of spacetime, challenging traditional views of gravity.
3. Action Functional and Holographic Properties: The paper explores the action principle for gravity and the peculiar role of surface terms in the context of horizons. It is argued that the surface terms in the gravitational action, although often disregarded, are deeply related to the entropy of horizons, hinting at a holographic principle in gravitational dynamics. Specifically, for Lanczos-Lovelock models, the entropy interpretation through Noether charge is expanded, encompassing more general theories beyond Einstein gravity.
4. Emergent Spacetime and Thermodynamic Description: Another insight presented is the emergent nature of spacetime, where gravity resembles macroscopic properties emerging from microscopic degrees of freedom—akin to thermodynamic properties arising from molecular motion in a gas. By considering spacetime as thermodynamic, the field equations of gravity can be interpreted as extremizations of an entropy functional, leading to potential simplifications in understanding cosmological conundrums, such as the cosmological constant problem.
5. Implications for Quantum Gravity: The arguments presented in the paper encourage further exploration into the implications for quantum gravity, where classical concepts of temperature and entropy may arise from deeper, quantum mechanical phenomena.

The paper speculates on future developments by suggesting that resolving the mysteries of black hole entropy and the thermodynamic nature of spacetime could lead to a unified understanding of gravity, thermodynamics, and quantum mechanics. Such an overview might not only clarify these foundational problems but also shape the next generation of theories in physics.