From spacetime thermodynamics to Weyl transverse gravity

There exist two consistent theories of self-interacting gravitons: general relativity and Weyl transverse gravity. The latter has the same classical solutions as general relativity but different local symmetries. We argue that Weyl transverse gravity also naturally arises from thermodynamic arguments. In particular, we show that thermodynamic equilibrium of local causal diamonds together with the strong equivalence principle encodes the gravitational dynamics of Weyl transverse gravity rather than general relativity. We obtain this result in a self-consistent way, verifying the validity of our initial assumptions, i.e., the proportionality between entropy and area and the different versions of the equivalence principle in Weyl transverse gravity. Furthermore, we extend the thermodynamic derivation of the equations of motion from Weyl transverse gravity to a class of modified theories of gravity with the same local symmetries. For this purpose, we employ the general expression for Wald entropy in such theories.