Thermodynamics of the apparent horizon in infrared modified Horava-Lifshitz gravity

Abstract

It is well known that by applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe, one can derive the corresponding Friedmann equations in Einstein, Gauss-Bonnet, and more general Lovelock gravity. Is this a generic feature of any gravitational theory? Is the prescription applicable to other gravities? In this paper we would like to address the above questions by examining the same procedure for Horava-Lifshitz gravity. We find that in Horava-Lifshitz gravity, this approach does not work and we fail to reproduce a corresponding Friedmann equation in this theory by applying the first law of thermodynamics on the apparent horizon, together with the appropriate expression for the entropy in Horava-Lifshitz gravity. The reason for this failure seems to be due to the fact that Horava-Lifshitz gravity is not diffeomorphism invariant, and thus, the corresponding field equation cannot be derived from the first law around horizon in the spacetime. Without this, it implies that the specific gravitational theory is not consistent, which shows an additional problematic feature of Horrava-Lifshitz gravity. Nevertheless, if we still take the area formula of geometric entropy and regard Horava-Lifshitz sector in the Friedmann equation as an effective dark radiation, we are able to extract the corresponding Friedmann equation from the first law of thermodynamics.

arXiv comment9 pages, the abstract, introduction and conclusions of the text were revised to remove text overlap with arXiv:hep-th/0602156 by other authors

References in corpus (38)

• Quantum Gravity at a Lifshitz Point
• Thermodynamics of Spacetime: The Einstein Equation of State
• On the Origin of Gravity and the Laws of Newton
• Thermodynamical Aspects of Gravity: New insights
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• Membranes at Quantum Criticality
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Non-equilibrium Thermodynamics of Spacetime
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Horava-Lifshitz Cosmology
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• The black hole and FRW geometries of non-relativistic gravity
• Strong coupling in Horava gravity
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Thermodynamic Behavior of Field Equations for f(R) Gravity
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Topological Black Holes in Horava-Lifshitz Gravity
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Thermodynamics of Black Holes in Horava-Lifshitz Gravity
• Symmetry Breaking Using Value Precedence
• Thermodynamics of interacting holographic dark energy with apparent horizon as an IR cutoff
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Thermodynamics of apparent horizon and modified Friedman equations
• Horizon Thermodynamics and Gravitational Field Equations in Horava-Lifshitz Gravity
• Thermodynamics of black holes in the deformed Hořava-Lifshitz gravity
• On the z=4 Horava-Lifshitz Gravity
• The generalized second law of thermodynamics in Horava-Lifshitz cosmology
• Scalar field perturbations in Horava-Lifshitz cosmology
• Entropy of black holes in the deformed Hořava-Lifshitz gravity
• Fermions Tunneling from Apparent Horizon of FRW Universe
• A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force
• Generalized uncertainty principle and Hořava-Lifshitz gravity
• Generalized uncertainty principle, quantum gravity and Hořava-Lifshitz gravity
• Thermodynamical Laws in Horava-Lifshitz Gravity

Cited by in corpus (12)

• Thermodynamics of Black Holes in Rastall Gravity
• Thermodynamic analysis of the static spherically symmetric field equations in Rastall theory
• Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
• Generalized Second Law of Thermodynamics in $f(T,T_G)$ gravity
• Lovelock gravity from entropic force
• Horizon Thermodynamics and Gravitational Field Equations in Quasi-Topological Gravity
• First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe
• Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon
• Thermodynamics of Quasi-Topological Cosmology
• Non-Local Deformation of a Supersymmetric Field Theory
• General Modified Friedmann Equations in Rainbow Flat Universe, by Thermodynamics
• Implications of maximum acceleration on dynamics