Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity

Abstract

We consider the Generalized Minimal Massive Gravity (GMMG) model in the first order formalism. We show that all the solutions of the Einstein gravity with negative cosmological constants solve the equations of motion of considered model. Then we find an expression for the off-shell conserved charges of this model. By considering the near horizon geometry of a three dimensional black hole in the Gaussian null coordinates, we find near horizon conserved charges and their algebra. The obtained algebra is centrally extended. By writing the algebra of conserved charges in terms of Fourier modes and considering the BTZ black hole solution as an example, one can see that the charge associated with rotations along ${\mathcal{Y}}_0$ coincides exactly with the angular momentum, and he charge associated with time translations ${\mathcal{T}}_0$ is the product of the black hole entropy and its temperature. As we expect, in the limit when the GMMG tends to the Einstein gravity, all the result we obtain in this paper reduce to the result of the paper \cite{5}.

14 pages

References in corpus (11)

• Massive Gravity in Three Dimensions
• Soft Heisenberg hair on black holes in three dimensions
• Black Hole Entropy in the presence of Chern-Simons Terms
• Minimal Massive 3D Gravity
• Matter coupling in 3D "Minimal Massive Gravity"
• Minimal Massive Gravity: Conserved Charges, Excitations and the Chiral Gravity Limit
• Black hole conserved charges in Generalized Minimal Massive Gravity
• The entropy formula of black holes in Minimal Massive Gravity and its application for BTZ black holes
• On Solutions of Minimal Massive 3D Gravity
• An alternative derivation of the Minimal massive 3D gravity
• Conserved Charges of Minimal Massive Gravity Coupled to Scalar Field

Cited by in corpus (22)

• Extended Symmetries at the Black Hole Horizon
• Spacetime structure near generic horizons and soft hair
• Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes
• Higher Spin Black Holes with Soft Hair
• Goldstone origin of black hole hair from supertranslations and criticality
• The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity
• Conserved Charges in Extended Theories of Gravity
• Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space
• Enhanced asymptotic $BM{S}_3$ algebra of the flat spacetime solutions of generalized minimal massive gravity
• General formulas for conserved charges and black hole entropy in Chern-Simons-like theories of gravity
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Symmetries near a generic charged null surface and associated algebra: an off-shell analysis
• Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Near Horizon Symmetry and Entropy Formula for Kerr-Newman (A)dS Black Holes
• Phase Transition Between Flat Space Cosmology and Hot Flat Spacetimes in GMMG and EGMG Models
• Linearized gravity and soft graviton theorem in de Sitter spacetime
• On Super-Translation transition between Quasi-local Black holes
• Hairy Black holes in General Minimal Massive Gravity
• Dynamical horizons and Super-Translation transitions of the horizon
• Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity
• Inducing supertranslations: The membrane picture