Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914173900816384 |
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| author | Bhandari, Gaurav Pathak, S. D. Ghotra, Harjit Khlopov, Maxim Yu Krasnov, Maxim A. |
| author_facet | Bhandari, Gaurav Pathak, S. D. Ghotra, Harjit Khlopov, Maxim Yu Krasnov, Maxim A. |
| contents | We derive generalized geodesic equations in curved spacetime that include conservative forces, dissipative effects, and quantum-gravity-motivated minimal-length corrections. Conservative interactions are incorporated through external vector potentials, while dissipative dynamics arise from an exponential rescaling of the particle Lagrangian. Phenomenological study of Quantum-gravity effects is introduced via Generalized Uncertainty Principle (GUP) deformed Poisson brackets in the Hamiltonian framework. We show that free-particle geodesics remain unaffected at leading order, but external potentials induce velocity-dependent corrections, implying possible violations of the equivalence principle. As an application, we analyze modified trajectories in Friedmann-Lemaitre-Robertson-Walker (FLRW) universes dominated by dust, radiation, stiff matter, and dark energy. Our results establish a unified approach to conservative, dissipative, and GUP-corrected geodesics, providing a framework to probe the interplay between external forces, spacetime curvature, and Planck-scale physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects Bhandari, Gaurav Pathak, S. D. Ghotra, Harjit Khlopov, Maxim Yu Krasnov, Maxim A. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics We derive generalized geodesic equations in curved spacetime that include conservative forces, dissipative effects, and quantum-gravity-motivated minimal-length corrections. Conservative interactions are incorporated through external vector potentials, while dissipative dynamics arise from an exponential rescaling of the particle Lagrangian. Phenomenological study of Quantum-gravity effects is introduced via Generalized Uncertainty Principle (GUP) deformed Poisson brackets in the Hamiltonian framework. We show that free-particle geodesics remain unaffected at leading order, but external potentials induce velocity-dependent corrections, implying possible violations of the equivalence principle. As an application, we analyze modified trajectories in Friedmann-Lemaitre-Robertson-Walker (FLRW) universes dominated by dust, radiation, stiff matter, and dark energy. Our results establish a unified approach to conservative, dissipative, and GUP-corrected geodesics, providing a framework to probe the interplay between external forces, spacetime curvature, and Planck-scale physics. |
| title | Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2509.14663 |