Conserved quantities and Virasoro algebra in New massive gravity

Abstract

Using the {\it off-shell} Noether current and potential we compute the entropy for the AdS black holes in new massive gravity. For the non-extremal BTZ black holes by implementing the so-called stretched horizon approach we reproduce the correct expression for the horizon entropy. For the extremal case, we adopt standard formalism in the AdS/CFT correspondence and reproduce the corresponding entropy by computing the central extension term on the asymptotic boundary of the near horizon geometry. We explicitly show the invariance of the angular momentum along the radial direction for extremal as well as non-extremal BTZ black holes in our model. Furthermore, we extend this invariance for the black holes in new massive gravity coupled with a scalar field, which correspond to the holographic renormalization group flow trajectory of the dual field theory. This provides another realization for the holographic c-theorem.

29 pages, Published version

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Cited by in corpus (17)

• Quasi-Local Conserved Charges in Covariant Theory of Gravity
• Quasilocal Conserved Charges with a Gravitational Chern-Simons Term
• Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity
• Novel relations in massive gravity at Hawking-Page transition
• Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy
• Thermodynamic and classical instability of AdS black holes in fourth-order gravity
• Noether current from surface term, Virasoro algebra and black hole entropy in bigravity
• Phase transitions of the BTZ black hole in new massive gravity
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Critical Heat Engines in Massive Gravity
• Static spheres and Aschenbach effect for black holes in massive gravity
• Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy
• Thermodynamics from field equations for black holes with multiple horizons
• Near horizon symmetry and entropy of black holes in $f(R)$ gravity and conformal gravity
• Existence of conserved quantities and their algebra in curved spacetime
• Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity
• Topological charge and black hole photon spheres in massive gravity