C-Functions in Lovelock Gravity

Abstract

We present C-functions for static and spherically symmetric spacetimes in Lovelock gravity theories. These functions are monotonically increasing functions of the outward radial coordinate and acquire their minima when evaluated on the horizon. Unlike the case of Einstein gravity, where there is a single C-function, we find that this function is non-unique in the case of Lovelock gravity. We define two C-functions, which agree at the horizon giving the black hole entropy, and state the different energy conditions that must hold in order for these functions to satisfy the monotonicity condition.

17 pages, 3 figures, v2-references added, few comments added

References in corpus (24)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Entropy of Lovelock Black Holes
• Black Hole Scan
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Non-Supersymmetric Attractors
• Conformal description of horizon's states
• Increase of Black Hole Entropy in Higher Curvature Gravity
• Geometric Holography, the Renormalization Group and the c-Theorem
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Black Holes in Pure Lovelock Gravities
• Black hole entropy in string-generated gravity models
• Universal regularization prescription for Lovelock AdS gravity
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Non-Supersymmetric Attractors and Entropy Function
• A C-Function For Non-Supersymmetric Attractors
• On black strings & branes in Lovelock gravity
• Holography, a covariant c-function, and the geometry of the renormalization group
• Black Hole Entropy from Horizon Conformal Field Theory
• Moduli flow and non-supersymmetric AdS attractors
• Horizon conformal entropy in Gauss-Bonnet gravity
• The Attractor Mechanism in Gauss-Bonnet Gravity
• Holography, The Second Law and a C-Function in Higher Curvature Gravity

Cited by in corpus (10)

• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Holographic c-theorems and higher derivative gravity
• Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities
• Lovelock black holes with non-constant curvature horizon
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Attractive holographic $c$-functions
• $c$-functions in Higher-derivative Flows Across Dimensions
• Domain Walls in Extended Lovelock Gravity
• Holographic RG Flows from Quasi-Topological Gravity
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows