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Title: Holography in action

Abstract

The 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 the Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes the Wald entropy on a horizon and the bulk term is the energy density (which is the Arnowitt-Deser-Misner Hamiltonian density for Einstein gravity). We show that this new pair also obeys a holographic relationship, and we give a thermodynamic interpretation of this relation in this context. Since the bulk and surface terms, in this decomposition, are related to the energy and entropy, the holographic conditionmore » 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.« less

Authors:
;  [1]
  1. IUCAA, Post Bag 4, Ganeshkhind, Pune 411 007 (India)
Publication Date:
OSTI Identifier:
21410138
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.82.024036; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DECOMPOSITION; DENSITY; ENERGY DENSITY; ENERGY DEPENDENCE; ENTROPY; GRAVITATION; HAMILTONIANS; HILBERT SPACE; HOLOGRAPHY; SURFACES; BANACH SPACE; CHEMICAL REACTIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; PHYSICAL PROPERTIES; QUANTUM OPERATORS; SPACE; THERMODYNAMIC PROPERTIES

Citation Formats

Kolekar, Sanved, and Padmanabhan, T. Holography in action. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.024036.
Kolekar, Sanved, & Padmanabhan, T. Holography in action. United States. https://doi.org/10.1103/PHYSREVD.82.024036
Kolekar, Sanved, and Padmanabhan, T. 2010. "Holography in action". United States. https://doi.org/10.1103/PHYSREVD.82.024036.
@article{osti_21410138,
title = {Holography in action},
author = {Kolekar, Sanved and Padmanabhan, T},
abstractNote = {The 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 the Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes the Wald entropy on a horizon and the bulk term is the energy density (which is the Arnowitt-Deser-Misner Hamiltonian density for Einstein gravity). We show that this new pair also obeys a holographic relationship, and we give a thermodynamic interpretation of this relation in this context. Since the bulk and surface terms, in this decomposition, are related to the 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.},
doi = {10.1103/PHYSREVD.82.024036},
url = {https://www.osti.gov/biblio/21410138}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 82,
place = {United States},
year = {Thu Jul 15 00:00:00 EDT 2010},
month = {Thu Jul 15 00:00:00 EDT 2010}
}