Electrically charged black hole on AdS${}_3$: scale invariance and the Smarr formula

Abstract

The Einstein-Maxwell theory with negative cosmological constant in three spacetime dimensions is considered. It is shown that the Smarr relation for the electrically charged BTZ black hole emerges from two different approaches based on the scaling symmetry of the asymptotic behaviour of the fields at infinity. In the first approach, we prove that the conservation law associated to the scale invariance of the action for a class of stationary and circularly symmetric configurations, allows to obtain the Smarr formula as long as a special set of holographic boundary conditions is satisfied. This particular set is singled out making the integrability conditions for the energy compatible with the scale invariance of the reduced action. In the second approach, it is explicitly shown that the Smarr formula is recovered through the Euler theorem for homogeneous functions, provided the same set of holographic boundary conditions is fulfilled.

arXiv comment14 pages, no figures

References in corpus (31)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Black Hole Entropy from Near-Horizon Microstates
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
• Charged Rotating Black Hole in Three Spacetime Dimensions
• Spinning charged BTZ black holes and self-dual particle-like solutions
• Generalized Black Holes in Three-dimensional Spacetime
• Lower-Dimensional Black Hole Chemistry
• Magnetic Solutions to 2+1 Gravity
• The electrically charged BTZ black hole with self(anti-self) dual Maxwell field
• Rotating magnetic solution in three dimensional Einstein gravity
• Critical behavior in 2+1 dimensional black holes
• Static Einstein-Maxwell Solutions in 2+1 dimensions
• Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions
• Comment on the Calculation of the Angular Momentum and Mass for the (Anti-) Self Dual Charged Spinning $BTZ$ Black Hole
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime
• Scale Invariant Hairy Black Holes
• On Magnetic solution to 2+1 Einstein--Maxwell gravity
• Flat space (higher spin) gravity with chemical potentials
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Black hole mass and angular momentum in 2+1 gravity
• Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; black holes
• Extremal limit for charged and rotating 2+1-dimensional black holes and Bertotti-Robinson geometry
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Asymptotic structure of the Einstein-Maxwell theory on AdS${}_3$
• Cardy formula for charged black holes with anisotropic scaling
• 2+1 dimensional charged black hole with (anti-)self dual Maxwell fields
• Superselection rule for the cosmological constant in three-dimensional spacetime
• On the First Law of Thermodynamics for (2+1) Dimensional Charged BTZ Black Hole and Charged de Sitter Space

Cited by in corpus (5)

• Phase transitions of black strings in dynamical Chern-Simons modified gravity
• BTZ black hole with KdV-type boundary conditions: Thermodynamics revisited
• Microscopic entropy of static black holes in 3d Lovelock gravities
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• The role of the cosmological constant as a pressure in the (2+1)-dimensional black string