Abstract
The gravitational Noether charge (Iyer-Wald) formalism has been shown to provide a systematic way to calculate conserved quantities, such as canonical energy or Wald entropy. Its original version applies to local, fully diffeomorphism invariant theories of gravity.
In my talk, I introduce an extension of the Noether charge formalism to local theories of gravity invariant under transverse diffeomorphisms and Weyl transformations. Among these theories, Weyl-transverse gravity is of particular interest, having the same classical solutions as general relativity.
However, the difference in symmetry group leads to a radiatively stable value of the cosmological constant. Given these attractive features of Weyl-transverse gravity, I discuss the application of our formalism to the first law of black hole mechanics and the Wald entropy formula 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.