Geodesic structure of spacetime near singularities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918507444174848 |
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| author | Mayank Kothawala, Dawood |
| author_facet | Mayank Kothawala, Dawood |
| contents | Geodesic flows emanating from an arbitrary point $\mathscr{P}$ in a manifold $\mathscr{M}$ carry important information about the geometric properties of $\mathscr{M}$. These flows are characterized by Synge's world function and van Vleck determinant - important bi-scalars that also characterize quantum description of physical systems in $\mathscr{M}$. If $\mathscr{P}$ is a regular point, these bi-scalars have well known expansions around their flat space expressions, quantifying \textit{local flatness} and equivalence principle. We show that, if $\mathscr{P}$ is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities. This yields remarkable insights into classical structure of spacetime singularities and provides useful tool to study their quantum structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12271 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geodesic structure of spacetime near singularities Mayank Kothawala, Dawood General Relativity and Quantum Cosmology Mathematical Physics Geodesic flows emanating from an arbitrary point $\mathscr{P}$ in a manifold $\mathscr{M}$ carry important information about the geometric properties of $\mathscr{M}$. These flows are characterized by Synge's world function and van Vleck determinant - important bi-scalars that also characterize quantum description of physical systems in $\mathscr{M}$. If $\mathscr{P}$ is a regular point, these bi-scalars have well known expansions around their flat space expressions, quantifying \textit{local flatness} and equivalence principle. We show that, if $\mathscr{P}$ is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities. This yields remarkable insights into classical structure of spacetime singularities and provides useful tool to study their quantum structure. |
| title | Geodesic structure of spacetime near singularities |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2512.12271 |