On a Gödel-like Solution in Non-Relativistic Gravity
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912907958157312 |
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| author | Santos, A. F. Amorim, R. G. G. Araújo, K. V. S. Ulhoa, S. C. |
| author_facet | Santos, A. F. Amorim, R. G. G. Araújo, K. V. S. Ulhoa, S. C. |
| contents | The article deals with Gödel-like solutions in the context of Galilean gravity, a geometric formulation of non-relativistic gravitation defined on a five-dimensional Galilean manifold. Within this framework, non-relativistic matter fields admit a covariant description, while the physical Newtonian dynamics is recovered through an immersion into the usual $3+1$ spacetime. By adopting a Gödel-like metric ansatz and coupling the gravitational field to a Galilean fluid derived from a variational principle, we obtain a system of highly nonlinear and coupled field equations. Exact solutions are constructed by fixing the matter sector consistently with the field equations. The resulting configurations describe rotating non-relativistic universes and satisfy $D(x)>H(x)$ throughout the entire spatial domain. As a consequence, the associated Killing vector remains spacelike everywhere and no closed timelike curves arise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Gödel-like Solution in Non-Relativistic Gravity Santos, A. F. Amorim, R. G. G. Araújo, K. V. S. Ulhoa, S. C. General Relativity and Quantum Cosmology The article deals with Gödel-like solutions in the context of Galilean gravity, a geometric formulation of non-relativistic gravitation defined on a five-dimensional Galilean manifold. Within this framework, non-relativistic matter fields admit a covariant description, while the physical Newtonian dynamics is recovered through an immersion into the usual $3+1$ spacetime. By adopting a Gödel-like metric ansatz and coupling the gravitational field to a Galilean fluid derived from a variational principle, we obtain a system of highly nonlinear and coupled field equations. Exact solutions are constructed by fixing the matter sector consistently with the field equations. The resulting configurations describe rotating non-relativistic universes and satisfy $D(x)>H(x)$ throughout the entire spatial domain. As a consequence, the associated Killing vector remains spacelike everywhere and no closed timelike curves arise. |
| title | On a Gödel-like Solution in Non-Relativistic Gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.14976 |