Non-linear equation of motion for higher curvature semiclassical gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912193217298432 |
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| author | Kumar, Naman |
| author_facet | Kumar, Naman |
| contents | 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 $\langle Q\rangle = T δS_{gen}$ where the heat-flux $\langle Q\rangle$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_10527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-linear equation of motion for higher curvature semiclassical gravity Kumar, Naman General Relativity and Quantum Cosmology High Energy Physics - Theory 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 $\langle Q\rangle = T δS_{gen}$ where the heat-flux $\langle Q\rangle$ 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. |
| title | Non-linear equation of motion for higher curvature semiclassical gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.10527 |