On non-equatorial embeddings into $\mathbb{R}^3$ of spherically symmetric wormholes with topological defects
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915678481547264 |
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| author | Cataldo, Mauricio Cuevas, Daniel |
| author_facet | Cataldo, Mauricio Cuevas, Daniel |
| contents | Traditionally, the embedding procedure for spherically symmetric spacetimes has been restricted to the equatorial plane $θ= π/2$. This conventional approach, however, encounters a fundamental limitation: not every spherically symmetric geometry admits an isometric embedding of its equatorial slice into three-dimensional Euclidean space. When such embeddings are not possible, the standard geometric intuition becomes inapplicable. In this work, we generalize the embedding procedure to slices with arbitrary polar angles $θ\neq π/2$, thereby extending the visualization and analysis of spacetimes beyond the reach of traditional methods.
The formalism is applied to Schwarzschild-like wormholes and to a generalized Minkowski spacetime with angular deficit or excess, which are particularly relevant since their equatorial slices cannot be consistently embedded in $\mathbb{R}^3$. In these cases, we identify the explicit constraints on the radial coordinate, polar angle, and geometric parameters required to guarantee consistent embeddings into three-dimensional Euclidean space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On non-equatorial embeddings into $\mathbb{R}^3$ of spherically symmetric wormholes with topological defects Cataldo, Mauricio Cuevas, Daniel General Relativity and Quantum Cosmology Traditionally, the embedding procedure for spherically symmetric spacetimes has been restricted to the equatorial plane $θ= π/2$. This conventional approach, however, encounters a fundamental limitation: not every spherically symmetric geometry admits an isometric embedding of its equatorial slice into three-dimensional Euclidean space. When such embeddings are not possible, the standard geometric intuition becomes inapplicable. In this work, we generalize the embedding procedure to slices with arbitrary polar angles $θ\neq π/2$, thereby extending the visualization and analysis of spacetimes beyond the reach of traditional methods. The formalism is applied to Schwarzschild-like wormholes and to a generalized Minkowski spacetime with angular deficit or excess, which are particularly relevant since their equatorial slices cannot be consistently embedded in $\mathbb{R}^3$. In these cases, we identify the explicit constraints on the radial coordinate, polar angle, and geometric parameters required to guarantee consistent embeddings into three-dimensional Euclidean space. |
| title | On non-equatorial embeddings into $\mathbb{R}^3$ of spherically symmetric wormholes with topological defects |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.13942 |