Noether-Wald energy in Critical Gravity

Abstract

Criticality represents a specific point in the parameter space of a higher-derivative gravity theory, where the linearized field equations become degenerate. In 4D Critical Gravity, the Lagrangian contains a Weyl-squared term, which does not modify the asymptotic form of the curvature. The Weyl${}^2$ coupling is chosen such that it eliminates the massive scalar mode and it renders the massive spin-2 mode massless. In doing so, the theory turns consistent around the critical point. Here, we employ the Noether-Wald method to derive the conserved quantities for the action of Critical Gravity. It is manifest from this energy definition that, at the critical point, the mass is identically zero for Einstein spacetimes, what is a defining property of the theory. As the entropy is obtained from the Noether-Wald charges at the horizon, it is evident that it also vanishes for any Einstein black hole.

7 pages, no figures, Final version for PLB

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Cited by in corpus (11)

• Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes
• Energy in Higher-Derivative Gravity via Topological Regularization
• Conformal renormalization of scalar-tensor theories
• Noether-Wald charges in six-dimensional Critical Gravity
• Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories
• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Topological invariants and the definition of energy in quadratic gravity theory
• Holographic correlation functions in Critical Gravity
• Lifshitz black holes in four-dimensional Critical Gravity
• Thermodynamics of non-linearly charged Anti-de Sitter black holes in four-dimensional Critical Gravity
• Nonconformally Ricci-flat instantons in Conformal Gravity with and without nonlinear matter fields