Abstract
The gravitational Noether charge (Iyer-Wald) formalism has been shown to provide a systematic way to calculate conserved quantities, such as energy, angular momentum or entropy, in theories of gravity. The original version of it applies to local, fully diffeomorphism invariant theories obtaining, as mostt known outcome, the Wald entropy formula.
In my talk, I introduce an extension of the gravitational Noether formalism to local theories of gravity invariant under transverse diffeomorphisms and Weyl transformations. Among these theories, Weyl transverse gravity is of particular interest.
It has the same classical solutions as general relativity, but the behaviour of the cosmological constant differs. Most notably, its value turns out to be unrelated to the vacuum energy density and radiatively stable.
Given these attractive features of Weyl transverse gravity, I discuss the application of our formalism to deriving the first law of black hole mechanics in this theory. Especially, I focus on the contributions coming from the cosmological constant and from possible violations of local energy conservation, which are in principle allowed in Weyl transverse gravity.
Finally, I will discuss the application of this theory to some current thermodynamics features of gravity.