Black hole entropy in the Chern-Simons-like theories of gravity and Lorentz-diffeomorphism Noether charge

Abstract

In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method \cite{3}. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern-Simons-like theories of gravity (CSLTG) and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.

13 pages, we have improved language of the paper

References in corpus (8)

• Massive Gravity in Three Dimensions
• Black Hole Entropy in the presence of Chern-Simons Terms
• Minimal Massive 3D Gravity
• Black hole entropy and Lorentz-diffeomorphism Noether charge
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• On the Generalized Massive Gravity in $Ad{S}_3$
• The entropy formula of black holes in Minimal Massive Gravity and its application for BTZ black holes
• On the new version of Generalized Zwei-Dreibein Gravity

Cited by in corpus (19)

• Conserved Charges in Extended Theories of Gravity
• The Heisenberg algebra as near horizon symmetry of the black flower solutions of Chern-Simons-like theories of gravity
• Revisiting Conserved Charges in Higher Curvature Gravitational Theories
• Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity
• On asymptotic charges in 3D gravity
• Lorentz-diffeomorphism Conserved Charges And Virasoro Algebra In Chern-Simons-Like Theories Of Gravity
• 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
• Lee-Wald Charge and Asymptotic Behaviors of the Weyl-invariant Topologically Massive Gravity
• Quasi-local conserved charges in Lorentz-diffeomorphism covariant theory of gravity
• Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
• Circularly symmetric solutions of Minimal Massive Gravity at its merger point
• Quasilocal first law of black hole dynamics from local Lorentz transformations
• Geometrothermodynamics for Black holes and de Sitter Space
• Quasi-Local Conserved Charges of Spin-3 Topologically Massive Gravity
• Mass and angular momentum of black holes in 3D gravity theories with first order formalism
• Quasi-local Energy in 3D Gravity with Torsion
• First Law of Inner Mechanics of Black Holes in Generalized Minimal Massive Gravity
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory