Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity

Abstract

Recently, it was discovered that lower-dimensional versions of Lovelock gravity exist as scalar-tensor theories that are examples of Horndeski gravity. We study the thermodynamics of the static black hole solutions in these theories up to cubic order through Euclidean methods. Considering solutions with spherical, planar and hyperbolic event horizons ($k=+1,0,-1$), we show that the universality of the thermodynamics for planar black holes ($k=0$) and the extended 1st law that include the variation of the couplings together with their associated potentials hold also in lower dimensions. We find that in $D=4,6$ where the 2nd- and the 3rd-order Lovelock Lagrangians are boundary terms respectively, the Smarr relation is modified since the entropy is not a homogenous function in these dimensions. We also present a derivation of the Smarr relation and its modified version based on the global scaling properties of the reduced action that is used to obtain the solutions consistently. Unlike the other hairy black hole solutions that have been analyzed before, despite the terms in the reduced action that break the scaling symmetry, the derivation still follows from a conserved Noether charge.

Version to appear in NPB

References in corpus (16)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Horndeski theory and beyond: a review
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Komar Integrals in Higher (and Lower) Derivative Gravity
• Thermodynamics of a BTZ black hole solution with an Horndeski source
• Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes
• Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes
• Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity
• Electrically charged black hole on AdS${}_3$: scale invariance and the Smarr formula
• No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity
• Revisit to Thermodynamic Relations in the AdS/CMT Models
• Can Bekenstein's area law prevail in modified theories of gravity?

Cited by in corpus (4)

• Regular BTZ black holes from an infinite tower of corrections
• Microscopic entropy of static black holes in 3d Lovelock gravities
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling