Kumar, NamanNamanKumar2025-08-312025-08-312025-02-0110.1016/j.physletb.2025.1392642-s2.0-85215085764http://repository.iitgn.ac.in/handle/IITG2025/28263We derive the non-linear semiclassical equation of motion for a general diffeomorphism-invariant theory of gravity by leveraging the thermodynamic properties of closed causal horizons. Our work employs two complementary approaches. The first approach utilizes perturbative quantum gravity applied to a Rindler horizon. The result is then mapped to a stretched light cone, which can be understood as a union of Rindler planes. Here, we adopt the semiclassical physical process formulation, encapsulated by 〈Q〉=TδS<inf>gen</inf> where the heat-flux 〈Q〉 is related to the expectation value of stress-energy tensor T<inf>ab</inf> and S<inf>gen</inf> is the generalized entropy. The second approach introduces a “higher curvature” Raychaudhuri equation, where the vanishing of the quantum expansion Θ pointwise as required by restricted quantum focusing establishes an equilibrium condition, δS<inf>gen</inf>=0, at the null boundary of a causal diamond. While previous studies have only derived the linearized semiclassical equation of motion for higher curvature gravity, our work resolves this limitation by providing a fully non-linear formulation without invoking holography.trueCausal diamond | Entanglement equilibrium | Generalized entropy | Higher curvature gravity | Perturbative quantum gravity | Stretched light coneArticlehttps://doi.org/10.1016/j.physletb.2025.139264February 20250139264arJournal0