Holography in Action
arXiv:1005.0619 · doi:10.1103/PhysRevD.82.024036
Abstract
Einstein-Hilbert action and its natural generalizations to higher dimensions (like the Lanczos-Lovelock action) have certain peculiar features. All of them can be separated into a bulk and a surface term, with a specific ("holographic") relationship between the two, so that either term can be used to extract information about the other. Further, the surface term leads to entropy of the horizons on-shell. It has been argued in the past that these features are impossible to understand in the conventional approach but find a natural explanation if we consider gravity as an emergent phenomenon. We provide further support for this point of view in this paper. We describe an alternative decomposition of the Einstein-Hilbert action and Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes Wald entropy on a horizon and the bulk term is the energy density (which is the ADM Hamiltonian density for Einstein gravity). We show that this new pair also obeys a holographic relationship and give a thermodynamic interpretation to this relation in this context. Since the bulk and surface terms, in this decomposition, are related to energy and entropy, the holographic condition can be thought of as analogous to inverting the expression for entropy given as a function of energy S = S(E,V) to obtain the energy E = E(S,V) in terms of the entropy in a normal thermodynamic system. Thus the holographic nature of the action allows us to relate the descriptions of the same system in terms of two different thermodynamic potentials. Some further possible generalizations and implications are discussed.
12 pages
References in corpus (24)
- Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
- Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
- Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
- Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
- Dark Energy and Gravity
- Hawking Radiation of Apparent Horizon in a FRW Universe
- Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
- Corrected Entropy-Area Relation and Modified Friedmann Equations
- Friedmann Equations and Thermodynamics of Apparent Horizons
- Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
- Thermodynamics of Apparent Horizon in Brane World Scenario
- Entropy of Null Surfaces and Dynamics of Spacetime
- Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
- Entropic Corrections to Friedmann Equations
- Holography of Gravitational Action Functionals
- The generalized second law of thermodynamics in generalized gravity theories
- F(R) gravity equation of state
- Thermodynamics of Apparent Horizon in Brane World Scenarios
- Thermodynamics of Einstein-Born-Infeld black holes with negative cosmological constant
- Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
- Gravity: A New Holographic Perspective
- Thermodynamics on the apparent horizon in generalized gravity theories
- Counterterms in Dimensionally Continued AdS Gravity
- Measurement of Quantum Fluctuations in Geometry