Evolution of spacetime arises due to the departure from holographic equipartition in all Lanczos-Lovelock theories of gravity

2014/08/31 by Sumanta Chakraborty, T. Padmanabhan, Τ. Padmanabhan · 55 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Degrees of freedom (physics and chemistry) #Einstein #Einstein field equations #Entropy (arrow of time) #Equipartition theorem #Gravitation #Mathematical physics #Minkowski space #Noether's theorem #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #Theoretical physics #gr-qc

paper · pdf · doi:10.1103/physrevd.90.124017

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(12) (American Physical Society) · v2, References Modified

openalex publication_date 2014/12/03 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In the case of general relativity, one can interpret the Noether charge in any bulk region as the heat content TS of its boundary surface. Furthermore, the time evolution of the spacetime metric in Einstein's theory arises due to the difference (N_sur\ensuremath-N_bulk) of suitably defined surface and bulk degrees of freedom. We show that this thermodynamic interpretation generalizes in a natural fashion to all Lanczos-Lovelock models of gravity. The Noether charge, related to the time evolution vector field, in a bulk region of space is equal to the heat content TS of the boundary surface with the temperature T defined by using local Rindler observers and S being the Wald entropy. Using the Wald entropy to define the surface degrees of freedom N_sur and the Komar energy density to define the bulk degrees of freedom N_bulk, we can also show that the time evolution of the geometry is sourced by (N_sur\ensuremath-N_bulk). When it is possible to choose the foliation of spacetime such that the metric is independent of time, the above dynamical equation yields the holographic equipartition for Lanczos-Lovelock gravity with N_sur=N_bulk. The implications are discussed.

Citations

• Superfluid analogies of cosmological phenomena
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Black holes and thermodynamics
• Thermodynamics of Spacetime: The Einstein Equation of State
• Structure of Lanczos-Lovelock Lagrangians in critical dimensions
• The Thermodynamics of Black Holes
• Particle creation by black holes
• Quantum Geometry and Black Hole Entropy
• Generalized second law of thermodynamics in black-hole physics
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Holes and Entropy
• Equipartition of energy in the horizon degrees of freedom and the emergence of gravity

Cited by

• Buchdahl compactness limit for a pure Lovelock static fluid star
• Emergent gravity paradigm: Recent progress
• A study of Universal thermodynamics in Lanczos–Lovelock gravity
• Distribution Function of the Atoms of Spacetime and the Nature of Gravity
• Generalized pure Lovelock gravity