On the Limitations of a Generalized Vaidya Metric
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914153188294656 |
|---|---|
| author | Chakrabarti, Soumya Dadhich, Naresh Singha, Chiranjeeb |
| author_facet | Chakrabarti, Soumya Dadhich, Naresh Singha, Chiranjeeb |
| contents | We prove that there can not be a smooth matching of the Generalized Vaidya metric with an exterior Schwarzschild/Vaidya patch across a finite boundary hypersurface unless the mass function is a function of the null coordinate alone. By explicitly deriving the extrinsic curvature components, we show that for $\partial m / \partial r \neq 0$ one has a discontinuity in the curvature and induces a surface stress-energy tensor, corresponding to a thin shell of matter. This discontinuity also appears in the geometric invariant $\mathcal{K} = K_{ab}K^{ab}$ and in the Kodama current, indicating a mismatch in quasi-local energy flux across the boundary. The analysis of timelike geodesics leads to the same condition, reinforcing that the generalized Vaidya geometry with $\partial m / \partial r \neq 0$ cannot represent a consistent stellar interior bounded by a regular surface. We therefore note that the generalized Vaidya spacetime should be interpreted as an unbounded geometry with intrinsic heat flux rather than a viable bounded source. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Limitations of a Generalized Vaidya Metric Chakrabarti, Soumya Dadhich, Naresh Singha, Chiranjeeb General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We prove that there can not be a smooth matching of the Generalized Vaidya metric with an exterior Schwarzschild/Vaidya patch across a finite boundary hypersurface unless the mass function is a function of the null coordinate alone. By explicitly deriving the extrinsic curvature components, we show that for $\partial m / \partial r \neq 0$ one has a discontinuity in the curvature and induces a surface stress-energy tensor, corresponding to a thin shell of matter. This discontinuity also appears in the geometric invariant $\mathcal{K} = K_{ab}K^{ab}$ and in the Kodama current, indicating a mismatch in quasi-local energy flux across the boundary. The analysis of timelike geodesics leads to the same condition, reinforcing that the generalized Vaidya geometry with $\partial m / \partial r \neq 0$ cannot represent a consistent stellar interior bounded by a regular surface. We therefore note that the generalized Vaidya spacetime should be interpreted as an unbounded geometry with intrinsic heat flux rather than a viable bounded source. |
| title | On the Limitations of a Generalized Vaidya Metric |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2511.09011 |