Lee-Wald charge and asymptotic behaviors of the Weyl-invariant topologically massive gravity

Abstract

<jats:title>Abstract</jats:title> <jats:p>We apply the Lee–Wald covariant phase space method to the Weyl-invariant topologically massive gravity and compute the corresponding on-shell conserved charges. By using appropriate decay conditions for the existing propagating modes in the near-horizon of a stationary black hole, we obtain the charges generating the asymptotic symmetries. We show that the charges are integrable and the (modified) algebras among the asymptotic generators are <jats:italic>closed</jats:italic> for the certain choice of central extensions.</jats:p>