Non-linear equation of motion for higher curvature semiclassical gravity
arXiv:2501.10527 · doi:10.1016/j.physletb.2025.139264
Abstract
We 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 where the heat-flux is related to the expectation value of stress-energy tensor and 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, \(δS_{\text{gen}} = 0\), 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.
arXiv comment7 pages, 3 figures. Accepted in Physics Letters B
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