Extend the QLH first law beyond general relativity

Extend the first law of mechanics for weakly isolated horizon segments in the quasi-local horizon framework to general metric theories of gravity beyond general relativity, identifying the appropriate horizon energy, surface gravity, and angular velocity observables and specifying assumptions under which the law holds.

Background

The review develops a Hamiltonian derivation of the first law for weakly isolated horizons (WIHs) entirely within general relativity, yielding a relation among horizon energy, surface gravity, area, and angular momentum defined intrinsically at the horizon. This first law is contrasted with the Iyer–Wald framework, which applies broadly (including higher-derivative theories) but relies on stationary backgrounds and bifurcate Killing horizons, making it less suitable for dynamical contexts addressed by the QLH approach.

Because WIHs and isolated horizons (IHs) are defined geometrically without reference to global Killing fields, and because the zeroth law holds in metric theories beyond GR for WIHs, it is natural to ask whether the QLH first law can be generalized to other metric theories. A successful extension would provide a physically robust dynamical law compatible with non-GR theories used in gravitational-wave phenomenology.