Remarks on the consistency of minimal deviations from General Relativity

TL;DR

This paper explores the implications of modifying General Relativity by breaking full diffeomorphism invariance, analyzing the resulting phase space sectors, solutions, and physical concerns such as thermodynamics and vacuum structure.

Contribution

It investigates the phase space structure and solutions of a modified gravity theory with broken diffeomorphism invariance, highlighting the existence of solutions and physical issues.

Findings

Existence of sectors with infinite constraints

Presence of known black hole and cosmological solutions

Physical concerns about thermodynamics and vacuum structure

Abstract

We study the consequences of the modification of the phase space structure of General Relativity imposed by breaking the full diffeomorphism invariance but retaining the time foliation preserving diffeomorphisms. We examine the different sectors in phase space that satisfy the new structure of constraints. For some sectors we find an infinite tower of constraints. In spite of that, we also show that these sectors allow for solutions, among them some well known families of black hole and cosmologies which fulfill all the constraints. We raise some physical concerns on the consequences of an absolute Galilean time, on the thermodynamical pathologies of such models and on their unusual vacuum structure.