Non-linear equation of motion for higher curvature semiclassical gravity

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 $⟨Q⟩=T\delta S_{gen}$ where the heat-flux $⟨Q⟩$ is related to the expectation value of stress-energy tensor $T_{ab}$ and $S_{gen}$ 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.

7 pages, 3 figures. Accepted in Physics Letters B

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Cited by in corpus (1)

• Investigating the shadows of new regular black holes with a Minkowski core: Effects of spherical accretion and core type differences