Interpret second-law terms in alternative metric theories

Determine the physical interpretation of the integrals in the quasi-local second-law identity for space-like DHSs in alternative metric theories of gravity (such as f(R) and scalar–tensor theories), identifying whether they represent meaningful energy fluxes or other local physical quantities.

Background

By substituting the Einstein tensor for matter stress-energy in the DHS second-law identity, the review derives a purely geometric balance law that holds in any metric theory, relating area change to curvature and shear terms. However, outside GR there is no guarantee that R/(2G) is a viable quasi-local mass nor that the right-hand side integrals represent energy flux.

Since f(R) and scalar–tensor theories figure prominently in gravitational-wave modeling, clarifying the physical meaning of these terms in such theories would bridge geometric identities with measurable fluxes.