Thermodynamics of spacetime and unimodular gravity

In this review we discuss emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation.
Comment: 19 pages, 2 figures. Review prepared for a Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity 2021. Version accepted by IJGMMP