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 closed for the certain choice of central extensions. We also find a particular static black hole solution for the Weyl-gauged Topologically Massive Gravity throughout our study.

中文翻译：

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Lee-Wald 电荷和外尔不变拓扑质量引力的渐近行为

我们将 Lee-Wald 协变相空间方法应用于 Weyl-invariant Topologically Massive Gravity 并计算相应的壳上守恒电荷。通过对静止黑洞近视域中现有的传播模式使用适当的衰减条件，我们获得了产生渐近对称性的电荷。我们表明电荷是可积的，并且渐近生成器之间的（修改的）代数对于中心扩展的某些选择是封闭的。在整个研究过程中，我们还为外尔测量的拓扑大质量引力找到了一个特定的静态黑洞解决方案。