Thermodynamics of spacetime and unimodular gravity

Abstract

In this review, we discuss the emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from the 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.