Generalised focusing theorem and dynamical horizon entropy in diffeomorphism-invariant theories

Abstract: I summarise recent progress on light-ray focusing and horizon thermodynamics in general diffeomorphism-invariant theories of gravity coupled to bosonic matter. In pure gravity and with scalar or vector fields, the null-null gravitational equation of motion on a linearly perturbed Killing horizon generalises the Raychaudhuri equation, defining a generalised expansion that never increases under the null energy condition. This proves a generalised focusing theorem and defines an increasing horizon entropy (Wall entropy). When higher-spin fields are present, the generalised focusing theorem persists subject to a "higher-spin focusing condition", which I propose as a physical consistency constraint on higher-spin theories.