Einstein's Equations from the Informational Action Principle
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866901722460323840 |
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| author | Boman, Erik Arne |
| author_facet | Boman, Erik Arne |
| contents | <p>This paper derives Einstein’s field equations from the Informational Action Principle (IAP), an information-geometric variational framework. The key result is that three independent ingredients — the Fisher-information identity for horizon entropy, a symplectic expression for the energy flux across local Rindler horizons, and an information-theoretic derivation of the Unruh temperature — together reproduce Jacobson’s thermodynamic argument for general relativity without assuming the area law, the heat equation, or the Unruh effect from the start.</p> <p>Under IAP dynamics, the generalized entropy of a local horizon evolves according to an information-driven gradient flow. Matter crossing the horizon provides the energy flux, the symplectic structure yields the correct form of delta Q, and IAP-induced decoherence sets the universal temperature proportional to acceleration. Combined with the Raychaudhuri focusing equation, these relations imply the Einstein field equations with a cosmological constant interpreted as a large-scale Fisher-information deficit.</p> <p>The result is a unified, information-theoretic reconstruction of general relativity, along with predicted quantum corrections to black hole physics and several open questions for future work.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17717136 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Einstein's Equations from the Informational Action Principle Boman, Erik Arne <p>This paper derives Einstein’s field equations from the Informational Action Principle (IAP), an information-geometric variational framework. The key result is that three independent ingredients — the Fisher-information identity for horizon entropy, a symplectic expression for the energy flux across local Rindler horizons, and an information-theoretic derivation of the Unruh temperature — together reproduce Jacobson’s thermodynamic argument for general relativity without assuming the area law, the heat equation, or the Unruh effect from the start.</p> <p>Under IAP dynamics, the generalized entropy of a local horizon evolves according to an information-driven gradient flow. Matter crossing the horizon provides the energy flux, the symplectic structure yields the correct form of delta Q, and IAP-induced decoherence sets the universal temperature proportional to acceleration. Combined with the Raychaudhuri focusing equation, these relations imply the Einstein field equations with a cosmological constant interpreted as a large-scale Fisher-information deficit.</p> <p>The result is a unified, information-theoretic reconstruction of general relativity, along with predicted quantum corrections to black hole physics and several open questions for future work.</p> |
| title | Einstein's Equations from the Informational Action Principle |
| url | https://doi.org/10.5281/zenodo.17717136 |